Dr. Robert A. Herrmann

Research Articles and Monographs.

Last revision 11 FEB 2016.


The following articles are written for specific audiences. All of my journal papers are "peer" reviewed by individuals who have judged that the material is correct and is appropriate for the interests of the journal's audience. Some of these papers fit more than one category. For your information, I have marked with the code (GID (GGU)) those papers that contain material that can be applied to the General Intelligent Design Theory (or Model) (GID). These can also be applied to the General Grand Unification Model, the GGU-model, since GID is an interpretation for this model. Much of the material in the GID marked papers can also be interpreted in a purely physical manner (the secular GGU-model). The code (OM) implies that these papers are also relevant to models that describe the origin of our universe. (Not all of the published and archived papers I have written are necessary listed here.)

Many of the following papers carry a copyright for the journal in which they appear. If you wish a copy for scholarship or research, the first method to secure a copy would be to place an order with Interlibrary Loan or a similar resource. If this is difficult for you to do, then I have scanned PDF reprints available. If this is the case, find the specific number and letter in the following list and then simply email your request using the subject heading "reprint." I will determine whether the request is for legitimate scholarship or research, and, hence, whether a copy will indeed be sent via returned e-mail as an attached file. If you receive a copy, then you will need to comply with all aspects of the appropriate copyright laws. Certain papers listed have non-descriptive titles. For these papers, an abstract is presented. Some of these abstracts may appear to be similar in character, but the material covered in the specific paper is either a different aspect of the specific topic discussed or the topic is explained from a different point of view. When you have read the abstract, please click on your browser's "return button" in order to return to this listing.

Further Remarks on Publication Requirements

When a paper is accepted for publication it must meet the requirements of a particular journal. By very definition and depending upon your status within the scientific community, you would almost never submit a paper mentioning or presenting an application of the presented material to theology or, due to the perceived relation between intelligent design and theology, the ID concept as well to secular refereed journals. By definition, a secular journal is for presentation of "secular" material. In mathematics, when a structure is constructed, the applications to other areas are often assumed to be "self-evident" and are generally not mentioned. If you want to apply your results to a "theological" subject, then this must be done in a different journal where the audience has such interests.

As of 2007, secular journal editors appear to be checking an author's interests via the Internet prior to even considering a paper in pure mathematics for publication. Unless the paper solves some well know problem, editors are now rejecting papers as being "inappropriate" based merely upon the author's theological associations. Not publishing in secular journals theological or GID interpreted material is not related to the quality of the work presented. It is related to the publication rules and, more recently, philosophy and forms of theological discrimination. Such discrimination is now being employed by reviewers for the arXiv.org archives. In the papers marked (GID(GGU)) or (OM), new concepts and methods within mathematics are presented. In only one (GID(GGU)) case, 18c, have I mentioned the self-evident fact that these results apply to a GID interpretation. Physical and theological applications for material presented within these papers appear elsewhere. Theological journals reject papers bases upon the relation of the researcher's results to doctrine. Within creationary science papers are also rejected based upon how a researcher's results counter models favored by the journal editors. Note: In the publication list C. R. S. = Creation Research Society

This article On Journal Publications gives further insight into paper journal publication.

Nonstandard and Infinitesimal Analysis

(21a) (GID(GGU)) "A special isomorphism between superstructures," Kobe J. Math., 10(2)(1993), 125-129.

(20a) "Consecutive points and nonstandard analysis," Math. Japonica 36(1991), 317-322.

(19a) (GID(GGU)) "Nonstandard consequence operators," Kobe J. Math., 4(1)(1987), 1-14 (MR89d:03068). Also at http://www.arxiv.org/abs/math.LO/9911204

(18a) "Supernear functions," Math. Japanica, 30(2) (1985), 169-185. (Erratum was published noting that Theorem 3.3 and Corollaries are in error. This has no effect on the other aspects of this paper.)

(17a) "A nonstandard approach to pseudotopological compactifications," Z. Math. Logik Grundlagen Math., 26(1980), 361-384. (MR82b:03113).

(16a) "Generalized continuity and generalized closed graphs,"Casopis Pest. Mat., 105(1980), 192-198. (MR81h:54057).

(15a) "Nonstandard implication algebras," Matematicki Vesnik, 3(16)(31)(1979), 403-411.

(14a) "Convergence spaces and nonstandard compactifications," Math. Rep. Academy of Science of Canada, 1(1979), 187-190. (MR80g:54058).

(13a) "Point monads and P-closed spaces," Notre Dame J. of Formal Logic, 20(1979), 395-400. (MR83c:54075).

(12a) "Perfect maps and remoteness,"Bull. Calcutta Math. Soc., 70(1978), 413-419. (MR81j:54082).

(11a) "Nonstandard implication algebras," Bulletin Mathematique dela Societe des Math., 2(15) (30)(1978), 351-358. (MR81f:03074).

(10a) "A nonstandard approach to S-closed spaces," Topology Proceedings, 3(1)(1978), 123-138.

(9a) "Theta-rigidity and the idempotent theta-closure," Math. Seminar Notes, 6(1978), 217-220. (MR80a:54004).

(8a) "The nonstandard theory of semi-uniform spaces," Z. Math. Logik Grudlagen Math., 24(3)(1978), 237-256. (MR58 #12992).

(7a) "Nonstandard quasi-Hausdorff, Urysohn, regular-closed extensions," Bull. Institute of Math., Academia Sinica, 5(1977), 13-25. (MR57 #7571).

(6a) "A nonstandard generalization for perfect maps," Z. Math. Logik Grundlagen Math., 23(1977), 223-236. (MR56 #5282).

(5a) "The productivity of generalized perfect maps," J. of the Indian Math. Soc., 41(1977), 375-386. (MR80d:54062).

(4a) "The theta and alpha monads in general topology," Kyungpook Math. J., 16(1976), 231-241. (MR55 #4125).

(3a) "The Q-topology, Whyburn type filters and the cluster set map," Proc. Amer. Math. Soc., 59(1976), 161-166. (MR58 #2785a,b).

(2a) "Nonstandard topological extensions," Bull. Australian Math. Soc., 13(1975), 260-290. (MR53 #9192a,b).

(1a) "A note on weakly-theta-continuous extensions," Glasnik Mat., 10(1975), 329-339. (MR53 #4037).

Standard General Topology

(12b) "Preconvergence compactness and P-closed spaces," International J. of Math. and Math. Sciences, 7((2)(1984), 303-310. (MR85i:540001).

(11b) "Closed graphs on convergence spaces," Glasnik Mat., 17(37)(1983), 461-465. (MR83j:00027).

(10b) "Extension of maps defined on a convergence space," Rocky Mt. J. Math., 12(1)(1982), 23-37. (MR83d:54023). A correction appears as an erratum in 16(3), 1986. The hypothesis of Theorem 4.4 is corrected and there are two obvious typos. in this erratum.

(9b) "Convergence spaces and closed graphs," Math. Rep. Academy of Science of Canada, 2(4)(1980), 203-208. (MR82g:54006).

(8b) "A note on convergence spaces and closed graphs," Proceedings of the Conference on Convergence Structures, Cameron University, (1980), 72-77. (MR82b:54006).

(7b) "RC convergence," Proc. Amer. Math. Soc., 75(1979), 311-317. (MR80c:54081).

(6b) "Perfect maps on convergence spaces," Bull. Australian Math. Soc., 20(1979), 447-466. (MR81c:54016).

(5b) "Convergence spaces and extensions of maps," Math. Rep. Academy of Science of Canada, 1(1979), 265-268.

(4b) "Convergence spaces and perfect maps," Math. Rep. Academy of Science of Canada, 1(1979), 145-148. (MR80e:54011).

(3b) "Maximum one-point near-compactifications," Boll. Un. Mat. Italiana, (5) 16A, (1979), 284-290. (MR80k:54036).

(2b) "One point near-compactifications," Boll. Un. Mat. Italiana, (5) 14A, (1977), 25-33. (MR55 #9030).

(1b) "Nearly-compact Hausdorff extensions," Glasnik Mat., 12(32)(1977), 125-132. (MR57 #1424).

Nonstandard and Infinitesimal Modeling

[Note: In some of the following papers, certain old MA-model terminology has been changed. This PDF file gives the correspondence between old and new terminology.]

Physical Science and Various GID(GGU)-model Related Papers

(26c) (OM) "The Relativity Monograph," C. R. S. Quarterly 30(March 1994)):186. Abstract 26c

(25c) (GID(GGU)) "The Eden Model.'' C. R. S. Quarterly 51(3)(Winter 2015):210. Abstract 25c

(24c) (GID(GGU)) "The GGU-model and Psalm 148:6," C. R. S. Quarterly 50(4)(Spring 2014):270-271. Abstract 24c

(23c) (GID(GGU)) "The Rapid Formation Model," C. R. S. Quarterly 50(1)(2013):48. Abstract 23c

(22c) (OM) "About Humphreys' 'New' Metric," Journal of Creation 23(3) (2009):50-52. Abstract 22c

(21c) (GID(GGU)) "The two meanings for modern intelligent design," Journal of Creation, 23(1)(2009):62-69.

(20c) (GID(GGU)) "General logic-systems and finite consequence operators,'' Logica Universalis, 1(2006):201-208. See http://www.arXiv.org/abs/math/0512559 Abstract 20c

(19c) (GID(GGU)) "The rationality of hypothesized immaterial mental processes," C. R. S. Quarterly 43(2)(2006):127-129 Abstract 19c

(18c) (GID(GGU)) "The best possible unification for any collection of physical theories,"Internat. J. Math. and Math. Sci., 17(2004):861-872. (Also see http://www.arXiv.org/abs/physics/0306147 ) and http://www.arXiv.org/abs/physics/0205073 Abstract 18c.

(17c) (GID(GGU)) "Hyperfinite and standard unifications for physical theories,"Internat. J. Math. and Math. Sci., 28(2)(2001):93-102. (Also see http://www.arXiv.org/abs/physics/0105012, where additions and a published correction to Theorem 5.3 is made. Note: The title in this version contains the additional word "all.") Abstract 17c.

(16c) (GID(GGU)) "Ultralogics and probability models," Internat. J. Math. and Math. Sci., 27(5)(2001):321-325. (See pages 15-17 in 13c below or http://www.arXiv.org/abs/quant-ph/0112037 where two published corrections are made in two statements.) Abstract 16c.

(15c) (GID(GGU)) "Information theory, consequence operators and the origin of life," C. R. S. Quarterly, 36(3)(1999):123-132. Abstract 15c.

(14c) (OM) "The NSP-World and Action-at-a-Distance." in Instantaneous Action at a Distance in Modern Physics: "Pro" and "Contra" Edited by Chubykalo, A., N. V. Pope and R. Smirnov-Rueda, (In CONTEMPORARY FUNDAMENTAL PHYSICS - V. V. Dvoeglazov (Ed.)) Nova Science Books and Journals, New York, (1999):223-235. Abstract 14c.

(13c) (GID(GGU)) "The Wondrous Design and Non-random Character of Chance Events." (1999) http://www.arxiv.org/abs/physics/9903038 Abstract 13c.

(12c) "Answers to three questions posed by Carl R. Froede Jr." C. R. S. Quarterly 35(4)(1999):234 Abstract 12c.

(11c) "A possible solution to the heat issue within catastrophic plate tectonics," C. R. S. Quarterly, 35(2)(1998):110-111 Abstract 11c.

(10c) "Newton's second law of motion holds in normed linear spaces," Far East J. Appl. Math. 2(3)(1998): 183-190 Abstract 10c.

(9c) "Deriving Vardiman's sedimentation equation," C.R.S. Quarterly, 34(2)(1997):103 and 34(3)(1997):173 Abstract 9c.

(8c) (OM) "A hypercontinuous hypersmooth Schwarzschild line element transformation," Internat. J. Math. and Math. Sci., 20(1)(1997):201-204 Abstract 8c.

(7c) (OM) "An Operator equation, and relativistic alternations in the time for radioactive decay," Internat. J. Math. and Math. Sci., 19(2)(1996):397-402 There are notational errors in the decay derivation. The derivation is corrected in my book and in http://arxiv.org/abs/physics/0312006 Abstract 7c.

(6c) (OM) "Operator equations, separation of variables and relativistic alterations," Internat. J. Math. and Math. Sci., 18(1)(1995):59-62 Abstract 6c. (Note: Last name misspelled (Hermann) on title page. But spelled correctly on interior pages.)

(5c) (OM) "Special Relativity and a nonstandard substratum," Speculations in Science and Technology, 17(1)(1994):2-10. Abstract 5c.

(4c) (OM) "Fractals and ultrasmooth microeffects," J. Math. Physics, 30(4), April 1989, 805-808. (MR#90d:03143) (See abstract for important typographical corrections.) Abstract 4c.

(3c) (GID(GGU)) "Physics is legislated by a cosmogony," Speculations in Science and Technology, 11(1) (1988), 17-24. Abstract 3c.

(2c) (GID(GGU)) "Subparticles and realism in quantum theories," C. R. S. Quarterly, 22(2)(1985), 84- 89. Abstract 2c.

(1c) "Rigorous infinitesimal modelling," Math. Japonica, 26(4)(1981), 461-465. (MR83j:00027).

Natural Systems and Cosmologies

(6d) "God, Hilbert, Weyl, Einstein, and Unifications," C. R. S. Quarterly 45(2), 140-141.

(5d) (GID(GGU)) "Simplifying the technical aspects of the G, D-world, MA-models and the U-cosmology," (1996), Electronically Published (This does not have a copyright. You may download and reproduce it as you like.)

(4d) (GID(GGU)) "World-views and the metamorphic model: their relation to the concept of variable constants," C. R. S. Quarterly 27(1)(1990), 10-15. Abstract 4d.

(3d) (GID(GGU)) "D-world evidence," C. R. S. Quarterly 23(2)(1986), 47-54. Abstract 3d.

(2d) (GID(GGU)) "Developmental paradigms," C. R. S. Quarterly, 22(4)(1986), 189-198. Abstract 2d.

(1d) (OM) "Mathematical philosophy and developmental processes," Nature and System, 5(1/2)(1983), 17-36. Abstract 1d.

Philosophical System Applications and Origins Science

(13e) (GID(GGU)) "GGU-model Ultra-logic-systems Applied to Developmental Paradigms" http://vixra.org/abs/1309.0004

(12e) (GID(GGU)) "Nonstandard ultra-logic-systems applied to the GGU-model," http://vixra.org/abs/1308.0125

(11e) (GID(GGU)) "On the GGU-model," American University Catalyst 9/1/2006. Abstract 11e,

(10e) (GID(GGU)) "The non-random character and intelligent design of 'chance' events," TJ, 15(2)(2001), 103-109. Abstract 10e.

(9e) (GID(GGU)) "A U-cosmology," (1996), Electronically Published (This does not have a copyright. You may download and reproduce it as you like. Further, some small improvements are being made. Note: This is a literal theological interpretation using secular GGU-model concepts. It appears that it may not be possible to differentiate, by any present day laboratory experimentation, between this scientific construct and those secular models accepted today by many individuals within the secular scientific community.)

(8e) (GID(GGU)) "Mathematical philosophy and evolution," ((1982) 1996), Electronically Published (Originally written for the U. S. Congress. This does not have a copyright. You may download and reproduce it as you like. Abstract 8e.)

(7e) "Incompleteness, creation-science and man made machines," C. R. S. Quarterly, 31(3)(1994), 148-152. Abstract 7e.

(6e) (GID(GGU)) "The scientific existence of a higher intelligence," C. R. S. Quarterly, 30(4)(1994), 218-222. Internet electronic version. Abstract 6e.

(5e) (GID(GGU)) "Ultrauniform," C. R. S. Quarterly, 30(4)(1993), 127. Abstract 5e.

(4e) "Metalogic Difficulties Associated with U. S. Supreme Court Opinion Roe V. Wade, 22 Jan. 1973," Inquiry Press, Niagara Falls, NY, (1985).

(3e) (GID(GGU)) "The word," C. R. S. Quarterly, 20(4)(1984), 226-229. Abstract 3e.

(2e) "The reasonableness of metaphysical evidence," J. of the Amer. Scientific Affiliation, 34(1)(1982), 12-23. Abstract 2e

(1e) "Gödel's Theorem Misunderstood." J. of the Amer. Scientific Affiliation, 33(4)(1981), 255.

Philosophy of Science

(2f) "Scientific premises?," C. R. S. Quarterly, 29(3)(1992), 160-161. Abstract 2f.

(1f) "Language and science," C. R. S. Quarterly, 22(3)(1985), 128-137. Abstract 1f.

Monographs and Books

(7g) "Logic for Everyone" http://arxiv.org/abs/math/0601709

(6g) "Nonstandard Analysis Applied to Special and General Relativity - The Theory of Infinitesimal Light-clocks," (2003) http://arxiv.org/abs/math/031218

(5g) "Nonstandard Analysis -A Simplified Approach," (2003) http://www.arxiv.org/abs/math.GM/0310351

(4g) (GID(GGU)) "Science Declares Our Universe is Intelligently Designed" (2002). Xulon Press, Fairfax, VA

(3g) (GID(GGU)) "Solutions to the 'General Grand Unification Problem,' and the Questions 'How Did Our Universe Come Into Being?' and 'Of What is Empty Space Composed?" Presented before the MAA, at Western Maryland College, 12 Nov. (1994) Abstract 1 or

(2g) (GID(GGU)) "The Theory of Ultralogics," (1993) this URL or Part I
and Part II at http://www.arxiv.org/abs/math.LO/9903082

(1g) "Some applications of nonstandard analysis to undergraduate mathematics: infinitesimal modeling and elementary physics," (1991) Instructional Development Project, Mathematics Department, U. S. Naval Academy, 572 Holloway Rd, Annapolis MD 21402-5002. Found at this URL or at the arXiv.

In the arXiv.org and viXra.org archives (some are repeated from above)

Generally listed (through 27) at http://arxiv.org/a/herrmann_r_1.

The archived articles after (29h) are listed at http://vixra.org/author/robert_a_herrmann

(29h) (GID(GGU)) "GGU-model Ultra-logic-systems Applied to Developmental Paradigms" http://vixra.org/abs/1309.0004

(28h) (GID(GGU)) "Nonstandard ultra-logic-systems applied to the GGU-model," http://vixra.org/abs/1308.0125

(27h) (GID(GGU)) "Modeling the dialectic" http://arxiv.org/abs/0810.0768

(26h) "Modern infinitesimal analysis applied to the physical metric dS and a theoretical verification of a time-dilation conjecture" http://arxiv.org/abs/0802.1809

(25h) (GID(GGU)) "The GGU-model and Generation of the Developmental Paradigms" (Originally at arXiv . This is the latest version. http://vixra.org/abs/1308.0145

(24h) "General logic-systems that determine significant collections of consequence operators" (This paper also contains a result that shows that, relative to classiacal logic, a set is constructed as potentially finite iff it is ordinary finite) http://www.arxiv.org/abs/math/0603573 Latest revision http://vixra.org/abs/1309.0013

(23h) "Logic for Everyone," http://www.arxiv.org/abs/math/0601709

(22h) (GID(GGU)) "General logic-systems and consequence operators," http://www.arxiv.org/abs/math/0512559

(21h) (GID(GGU)) "Nonstandard Consequence Operators Generated By Mixed Logic-Systems," http://www.arxiv.org/abs/math/0412562

(20h) "Nonstandard Analysis and Generalized Functions," http://www.arxiv.org/abs/math/0403303

(19h) "Nonstandard Analysis Applied to Advanced Undergraduate Mathematics - Infinitesimal Modeling," http://www.arxiv.org/abs/math/0312432

(18h) "Nonstandard Analysis Applied to Special and General Relativity - The Theory of Infinitesimal Light-Clocks," http://www.arxiv.org/abs/math/0312189

(17h) "A Hypercontinuous Hypersmooth Schwarzschild Line Element Transformation," http://www.arxiv.org/abs/math-ph/0312007

(16h) "Operations Equations, Separation of Variables and Relativistic Alterations," http://www.arxiv.org/abs/math-ph/0312005

(15h) "An Operator Equation and Relativistic Alterations in the Time for Radioactive Decay," http://www.arxiv.org/abs/math-ph/0312006

(14h) "Nonstandard Analysis - A Simplified Approach," http://www.arxiv.org/abs/math/0310351

(13h) (GID(GGU)) "The Best Possible Unification for Any Collection of Physical Theories," http://www.arxiv.org/abs/physics/0306147

(12h) "An Ultimate Hyperfinite Ultralogic Unification for all Physical Theories," http://www.arxiv.org/abs/physics/0205073

(11h) (GID(GGU)) "Probability Models and Ultralogics," http://www.arxiv.org/abs/quant-ph/0112037

(10h) "Standard and Hyperfinite Unifications for All Physical Theories," http://www.arxiv.org/abs/physics/0105012

(9h) (GID(GGU)) "An Ultralogic Unification for All Physical Theories," http://www.arxiv.org/abs/physics/0101009

(8h) "A Nonstandard Derivation for the Special Theory of Relativity," http://www.arxiv.org/abs/physics/0005031

(7h) (GID(GGU)) "Nonstandard Consequence Operators," http://www.arxiv.org/abs/math/9911204

(6h) (GID(GGU)) "The Encoding of Quantum State Information Within Subparticles," http://www.arxiv.org/abs/quant-ph/9909078

(5h) "General Relativity and Contrary Predictions," http://www.arxiv.org/abs/physics/9905040

(4h) (GID(GGU)) "The Wondrous Design and the Non-random Character of 'Chance' Events," http://www.arxiv.org/abs/physics/9903038

(3h) (GID(GGU)) "The Theory of Ultralogics Part II," http://www.arxiv.org/abs/math/9903082

(2h) (GID(GGU)) "The Theory of Ultralogics Part I," http://www.arxiv.org/abs/math/9903081

(1h) (GID(GGU)) "Solutions to the 'General Grand Unifications Problem," and the Questions 'How Did Our Universe Come into Being?'," http://www.arxiv.org/abs/astro-ph/9903110

Book Reviews (Considered as expository published articles.)

(6i) "Nonstandard Analysis," J. Ponstein, Research School Systems, Organisation and Management, (2001) for Zentralblatt für Mathematik (2003).

(5i) "Nonstandard Analysis for Working Mathematicians," P.A. Loeb and M. Wolf (Eds) (2000) for Zentralblatt für Mathematik (2001).

(4i) "Brownian Motion on Nested Fractals," T. Linstrom, Memoirs of the American Mathematical Society No. 420, Providence, RI (1990) for Zentralblatt für Mathematik (2001).

(3i) "Foundations of Infinitesimal Stochastic Analysis," K.D. Stroyan and J.M. Bayod, North-Holland, New York, (1986) for Zentralblatt für Mathematik (1987).

(2i) "Nonstandard Methods in Stochastic Analysis and Mathematical Physics," S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, T. Lindstrom, Academic Press, Orlando, FL (1987) for Zentralbatt für Mathematik (1987).

(1i) "Science and Scepticism," J. Watkins, Princeton University Press, Princeton (1984), in C. R. S. Quarterly 23(2)(1986), 74-75.

Return to home page.

This is the announcement of the monograph that has my derivations of metrics some of which correspond to Humphreys'. It predates Hymphreys' announcements.

This is a letter that partially describes the most strict creationary model known. The entire description appears http://vixra.org/abs/1409.0239 and on this website.

This is a letter that describes some of the intuitive foundations for modern mathematics, the Biblical meaning of such Old Testament terms as "for ever and ever" and how the GGU-model participator mechanism applies to this notion.

This is a brief letter that describes the technical process that rapidly forms an entire cosmology over what can be a zero observer time period.

A metric that Humphreys claims was new, was actually derived by me in 1993 and published in 1996. This short paper gives an improved derivation. This is a metric for a constant gravitation field. Humphreys is using this metric to describe a new cosmology.

Among other results, in this paper a significant result is to show that the notion of the finite consequence operator is equivalent to the notion of a logic-system. It is also shown, that there are infinitely many finite consequence operators that cannot be generated by a finite logic-system. Various significant examples are also given.

Nobel Laureate Sir John Eccles proposed that from a vast amount of evidence there appears to be real immaterial aspects for how the human "mind" behaves as these aspects are described by Popper. In this paper, mathematical models are discussed that show that such immaterial aspects are scientifically rational in character.

It is shown that the set of all finitary consequence operators defined on any nonempty language is a join-complete lattice. This results is applied to various collections of physical theories to obtain an unrestricted standard supremum unification. An unrestricted hyperfinite ultralogic unification for sets of physical theories is also obtained.

A set of physical theories is represented by a nonempty subset PH of the lattice of consequence operators defined on a language L. It is established that there exists a unifying injection Sw defined on the nonempty set of significant representations for natural systems M. If W is a member of M, then the image Sw(*W) is a ultralogic such that, when Sw(*W) is restricted to the language of the physical theories, the result is the same as each member of PH being applied to W. A "product" hyperfinite ultralogic P is defined on internal subsets of an n-order Cartesian produce of *L and shown to represent the application of S to any finite subset of M such that |M| = n. It is also shown that there exists a standard unifying injection on M and the images of this standard unifying are compared with the ultralogic images of the unifying injection S.

In this paper, we show how nonstandard consequence operators, ultralogics, can generate the general informational content displayed by probability models. In particular, a probability model that predicts that a specific single event will occur and those models that predict that a specific distribution of events will occur.

In this article, the Gitt (1997) concept of information as it is represented by a mental-like sequence of activities is compared with the mental activity represented by consequence operators. It is shown how consequence operators model mathematically these Gitt notions and how a specific ultralogic and four ultrawords yield an identical foundation for Gitt's information theory scenario for the origin of life. Consequence operator theory, as a model for Gitt information theory, is used to establish that, relative to this model and without external modification to the processes, it is not possible, using fixed pragmatic information, to increase or decrease the complexity of a biological entity by selecting from two distinct independently produced biological entities as these entities are characterized at the apobetic level. This signifies that if random mutations are random alterations in the characteristics of a biological entity that are, necessarily, not dependent upon the original biological characteristics, then this model would tend to disallow random mutations as a viable source for biological alterations. On the other hand, for fixed pragmatic information, an increase or decrease in complexity by selecting from two distinct apobetic level biological entities is possible if a very special dependency exists between their characteristics. Further, complexity can also be increased by applying the semantic level consequence operator to an increased portion of the information contained within the genetic code in the DNA, information that exists originally.

Using the Nonstandard Physical World (NSP-world) model, a model that cannot be eliminated from scientific discourse, it is predicted that specific processes exist such that information between objects within our natural environment would appear to be transmitted instantaneously. In this article, certain aspects of this model are discussed as well as experimental evidence that establishes as fact the model's prediction that a type of nonlocal instantaneous action-at-a-distance does occur in objective reality.

In this article, it is shown specifically that natural system chance events as represented by theory predicted (a priori) probabilistic statements used in such realms as modern particle physics, among others, are only random relative to the restricted language of the theory that predicts such behavior. It is shown that all such "chance" natural events are related one to another by a remarkably designed, systematic and wondrous collection of equations that model how the natural laws and processes specifically yield such natural events. A second result shows theoretically that all such "chance" behavior is caused by the application of well-defined ultralogics. These results show specifically that the fundamental underlying behavior associated with all natural systems that comprise our universe is controlled internally by processes that cannot be differentiated from those that mirror the behavior of an infinitely powerful mind.

In this letter, the questions, how rapidly did the heat generated dissipate?, what is the maximum temperature attained? and what physical processes were involved in the heat transfer? for the model proposed in 11c are answered in the only way such a model is capable of answering such specific questions.

In a recent publication, Carl R. Froede Jr. discussed the problem of the heat generated during the short Flood period by the processes know as catastrophic plate tectonics, CPT. The author states that the rapid removal of such energy is an unexplained aspect of the CPT model. However, ongoing theoretical research may give a possible solution to this and other problems such as the rates of radioactive decay. Using the linear effect line element and a pure complex substratum term, a type of "time compression" is obtained that would increase the rates for all modes of heat dispersal.

By application of elementary laboratory observations, Newton's Second Law of Motion is derived for any normed linear space. The derivation assumes that the same elementary physical observations made by Newton hold in a normed linear space and uses the elementary theory of Robinson infinitesimals. The theory of Robinson infinitesimals is a rigorous approach to the informal Newtonian theory of the infinitely little. [Note: A major typographical error appears in display (4), page 187. The lower case subscript "m" should be a capital "M" subscript.]

The Vardiman sedimentation equation for the ocean floor sediment is obtained from empirical evidence and data matching. In this paper, a derivation from first principles for this equation is obtained by considering a homogeneous mixing problem with relaxation time incorporated in order to smooth out discontinuous mixing. The differential equation obtained has a unique solution which is the Vardiman sedimentation equation.

In this paper, a new derivation for one of the black hole line elements is given since the basic derivation for this line element is flawed mathematically. This derivation postulates a transformation procedure that utilizes a transformation function that is modeled by an ideal nonstandard physical world transformation process that yields a connection between an exterior Schwarzschild line element and distinctly different interior line element. The transformation is an ideal transformation in that in the natural world the transformation is conceived of as occurring at an unknown moment in the evolution of a gravitationally collapsing spherical body with radius greater than but near to the Schwarzschild radius. An ideal transformation models this transformation in a manner independent of the objects standard radius. It yields predicted behavior based upon a Newtonian gravitational field prior to the transformation, predicted behavior after the transformation for a field internal to the Schwarzschild surface and predicted behavior with respect to field alteration processes during the transformation.

In this paper, using concepts from the nonstandard physical world, the linear effect line element is derived. Previously, this line element was employed to obtain, with the exception of radioactive decay, all of the experimentally verified special theory relativistic alterations in physical measures. This line element is now used to derive, by means of separation of variables, an expression that predicts the same increase in the decay time for radioactive material as that predicted by the Einstein time dilation assumption. This indicates that such an increase in lifetime can be attributed to an interaction of the radioactive material with a properton field rather than to a basic time dilation.

In this paper, a simple and unified method is developed that predicts the relativistic alterations of physical measures when the behavior of a natural system is characterized by means of a specific operator equation. Separation of variables is the simple underlying procedure. This method can be applied to both the Special and General Theories of relativity, among others.

Using properties of the nonstandard physical world, a new fundamental derivation for all of the effects of the Special Theory Relativity is given. This fundamental derivation leads to the basic expressions from which Prokhovnik derives the basic Special Theory transformations. However, the interpretations used in this new derivation are completely distinct from Prokhovnik's. Indeed, this derivation shows that the effects of the Special Theory are manifestations of the interaction between our natural world and a nonstandard properton substratum field. This derivation also eliminates the controversy associated with any physically unexplained universal time dilation and length contraction as well as the logical error of extrapolating the language of relativity to unrelated physical concepts.

In this paper, a portion of the nonstandard methods first introduced by Nottale and Schneider [J. Math. Phys 25, 1296 (1984)] for the investigation of fractal behavior are replaced by methods employing polysaturated enlargements. This process yields internal functions that are ultrasmooth and have a standard part equal to the original fractal. These ultrasmooth nonstandard functions also possess a well-behaved * integral length concept. Additionally, a method is presented that shows that if certain behavior is modeled after a simple finitely discontinuous step function, then this function is also the standard part of an internal hypersmooth nonstandard approximation. [The editors did not do a good job. Statement (ii) should read ". . . *-differentiable of order n . . . ." In the proof of Theorem 4.1, in equations hj(x,c,d), Gj(x), the ) + 1)) should be )) + 1). In Gj(x), the "c" should be replaced with aj. In the second column, second paragraph line six page 808, st(D) should be st(*D)and, trivially, x in μ(p) should read x in μ(p) ∩ *D. Of less importance is that in the proof of theorem 3.1, first line *Rm should read Rm.]

[This paper is entirely high level mathematics. The most important parts of this paper relative to origins research are the applications and Theorem 4.1. This theorem is used to model, within the NSP-world, a process that allows for "sudden change" of the behavior of a Natural system or "incomprehensible distortion" of the information received relative to such a sudden change.]

The known theoretical results entailed by the NSP-world model are applied to a cosmogony. This cosmogony is based on observations of de Broglie, Patton and Wheeler, among others, and a new method for mathematical modeling. This mathematically generated cosmogony forms our entire Universe, yields a describable process that brings our Universe and others into being, unifies all of the testable and empirical content of all known scientific theories, yields the possible non-theory entailed chaotic behaviour for various natural systems, satisfies the observer-participator quantum principle and exhibits an intrinsic source that appears to produce, sustain and guide all natural system behaviour. A self-interpreting feature of the mathematical structure automatically and without any imaginative interpretation generates the basic entities called subparticles [propertons] and their fundamental properties. Research has yielded a mechanism which indicates that subparticles [properton]) may be the fundamental substance of all material particles, fields and space itself and, thus, the major constituents for a pregeometry. (One of the best published papers explaining these concepts without extensive mathematical discourse.)

This is the first article in the series entitled "Nature: the Supreme Logician." I describe how new methods in mathematical logic automatically yield the logical existence of subparticles [propertons]. The necessity for subparticles [propertons] follows from the most basic logical operator that produces a describable change in the behavior of a natural system. Subparticles [Propertons] apparently yield a mediating structure for all quantum transitions, provide an actual substratum for relativistic and cosmological theories and may be the physical bases for a pregeometry. It is shown that subparticles [propertons], their application and their production by a supermind process [IUN-process] restore a universal causality and determinacy to systems that are describable by means of a quantum mechanical language, among others.

In this paper, the D-world model is used to discuss four scientific method presuppositions, involving linguistic concepts, that should be radically altered prior to the selection of any theory that incorporates variations in assumed universal constants. The metamorphic-anamorphosis (MA) model is re-introduced as an appropriate theoretical construct that is consistent with the four altered presuppositions.

This is the final article in the series "Nature: The Supreme Logician." This article discusses indirect evidence for the acceptance of the deductive-world [GD] model. The evidence includes the unification of certain incompatible logics internal to quantum mechanics, other physical theories and computer science; subparticle [properton] models for quantum transitions, the formation of elementary particles and fields, the local Special Theory and how such subparticle [properton] models explain the experimental results associated with the Bell inequality. It is shown how a special interpretation correlates the deductive-world [and MA] model to Scripture.

This is the third article in the series entitled "Nature: The Supreme Logician." In this article, the supermind [IUN] processes associated with the deductive-world [GD] [and MA-model] model are discussed. The specific object called the developmental paradigm is defined and its unique behavior is investigated. It is shown how this object and supermind [IUN] processes deterministically generate the entire universe in which we dwell as well as the fundamental constituents of all material microphysical, macrophysical and large scale structures. It is shown that the deductive-world [GD] [and MA-model] is a nontrivial grand unification. Using concepts of the supermind [IUN] choice and super[ultra]uniform alterations it is proved that the linguistic concepts of random behavior and random cause are theory (i.e. discipline language) dependent and are not absolute in character. This is the second paper that gives explicit examples for the design of universes, in general, by means of, what is now called, a deductive intelligence.

This paper discusses numerous concepts relative to mathematical modeling. It presents the MA-model solution to the discreteness paradox. In particular, a method is described that will eliminate this paradox for all theories. The method is applied to two cases where the paradox is associated with the classical continuum models and competing Feynman diagram models.

This is a short letter that discusses certain GGU and GID model properties.

In this article, recent advances in general design theory are discussed. In particular, a signature that implies that randomness is, in general, designed by a higher intelligence and that all natural-system behavior that is deemed as probabilistic in character is specifically designed, produced, co-ordinated and sustained by a higher intelligence. These conclusions are based upon an interpretation for mathematically obtained results and indirect evidence. Aspects of these results are related to the Scriptures.

This is the first paper written that uses the metamorphic portion of the MA-model as a viable modeling procedure. It is used to model the sudden appearance or alteration of biological entities.

In this article, in order to correct a few misconceptions, a simple yet in-depth discussion of the procedures, methods and results associated with Gödel type incompleteness theorems is given. In particular, the important concepts of formal and informal reasoning processes are discussed and illustrated. Further, information is compiled from the discipline of Mathematical Logic and elsewhere that gives exceedingly strong evidence that there are human mental processes that cannot be duplicated by a man-made machine.[Note: Important typographical error. Page 151, Column 2, line 8 and 9 from bottom. "informal" should read "formal."

This article gives a general overview of recent results in mathematical logic that should have a profound effect not only upon the foundations of creation-science but the foundations of all religious experiences and thought that either assume or logically require the existence of a supernatural higher intelligence. In particular, it is shown that the concept of the existence of a higher intelligence exterior to the material universe can be modeled rationally by means of the science of mathematics. It is established that human religious experiences and scientific models associated with either an assumption of or an implied requirement that a supernatural higher intelligence exists are not somehow or other irrational in character as it is claimed by many secular scientists and philosophers. Indeed, if such experiences or creation-science models directly correlate to certain customary Bible interpretations, then the assumption of irrationality is scientifically proved to be false.

The concept of ultrauniform is described in more detail. It is specifically related to two views of what constitutes uniform behavior. The human view and the Divine view.

This is the second paper published that gives a theological interpretation to a mathematical model. The first paper [The Reasonableness of Metaphysical Evidence, J. Amer. Scientific Affiliation, 34(1)(1982),pp. 12-23] uses a different model called the G-model. This article gives a summary of completed research into some of the logical processes required to accept and investigate such concepts as Divine creation, the miraculous and continual sustaining of our present universe. These logical concepts are directly related to Scriptural quotations. By applying new and powerful tools from applied mathematical logic it is established that all such concepts are absolutely rational and follow describable rational patterns. This is the first known paper that discusses in detail the intelligent design notion that is now called "deductive intelligence," a design produced by a "higher intelligence."

This article explains how a recent discovery in the science of mathematical logic has been employed to construct a scientific model for many of the major concepts in Christian doctrine. These results give strong scientific evidence that the basic foundation for the religious philosophy of Marxists, secular humanists, atheists and millions of individuals who reject Christianity is logically incorrect. The logical incorrectness of this foundation is grounded on the fact that it has been scientifically established that this foundation is based upon a mathematically refutable premise. [The G-model is used to establish these findings.]

In this "letter," the MA-model conclusion that theoretical science is based upon prior belief-systems is discussed.

This is the second article in the series entitled "Nature: the Supreme Logician." This article discusses various notions associated with the language of science. In particular, the concept of a rational description, hypotheses, indirect verification, theories, scientific speculation, discipline languages, Mill induction, improper theories, and the notion of a model are discussed. The concepts of falsifiability and hypothesis modification are delineated. One of the major features of this discussion is an introduction to what applied mathematical modeling truly signifies and an investigation into the unscientific methods, such as absolute randomness, that are utilized ad hoc to reject totally acceptable alternative scientific theories.

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