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As a former employee of the Federal Government, I must make the following books available free of charge since they were written using federal funds. These books are written in Plain Tex, the well-known technical word processor. The files have been reprocessed so that they can be "read" and printed by use of the Adobe Reader. With the exception of book 2, in order to save as much disk space as possible, the files have also been additionally compressed by means of zip software. The Adobe reader should only be considered as a "pre-viewer." Suggestions as to the best magnification for such viewing will be given on the "content" pages. However, the "reader" will yield excellent and perfectly printed copies at 300 DPI. [Note: There may be one or two instances were a standard Roman type "comma" has been translated into a capital Gamma.]If you find any of the files faulty, please E-mail me with an appropriate identification and I will attempt to correct the problem. I am aware that disk space may not now be available for you to download and "unzip" an entire book. The number that appears after each file's name is the unzipped pdf file size and the books have been constructed so that they may be easily reproduced in duplex form. As mentioned, I cannot sell these books to the general public since they were mostly financed by government funds.

BOOK 1 (2.048MB)

Logic for Everyone, (1994) Math. Dept., U. S. Naval Academy, Annapolis MD 21402-5002 (USA)

As far as I can tell, this is the most elementary book in Mathematical Logic available that also covers all of the basic material in the propositional and predicate calculus. This is the book written especially for the Midshipmen at the United States Naval Academy with the general view that it is a terminal course. Enough material is covered so that certain topics in elementary model theory can be included and all mathematical proofs are of the most elementary nature requiring no specialized mathematical procedures. Applications include a very elementary introduction to nonstandard models as they are obtained by means of the "compactness" theorem, and the generation of weak "ultrawords" and an "ultralogic" operator. A complete set of answers for all exercise problems and 6 figures in the form of gif images are included.

The following free book was under a research grant from the U. S. Naval Academy Research Council. (Unfortunately, it is probably not totally free from minor typographical errors.) It has been used by numerously many individuals throughout the world to teach themselves the new rigorous Robinson methods of infinitesimal analysis and the new rules for rigorous modeling. In particular, it has been used by scientists at NASA for this purpose.

Some Applications of Nonstandard Analysis to Advanced Undergraduate Mathematics -- Infinitesimal Modeling, Elementary Physics, Generalized Functions, (A $180 value) 1989-1991 Instructional Development Project, Math. Dept., U. S. Naval Academy, Annapolis MD 21402-5002 (USA)

This 217 page book is constructed in a somewhat unusual manner. It is composed of three "manuals". In the first manual, the rigorous rules and procedures are presented and examples are given as to their use. With the exception of chapter 9, the actual proofs of the mathematical theorems that are so applied appear in a series of appendices.

The second much smaller manual applies these rigorous methods to some areas in physics not covered in the first manual. Such things as an actual formal derivation of Newton's Second Law of motion from more fundamental observations is given. Certain methods used in physics that deal with the concept of point masses are shown to be incorrectly expressed in the language that appears in elementary texts and the proper concept is presented.

As an added feature, the third manual deals with a very significant concept within nonstandard analysis, not specifically identified previously, the enlargement and the saturation properties for a model. In order to give appropriate instruction in the use of such concepts, they are applied to the important scientific and mathematical subject known as generalized functions or distributions.

The Theory of Ultralogics, (1993) Institute for Mathematics and Philosophy (Corrections and improvements are being made to this book. Due to discrimination now being practiced by the arXiv.org archives, the version presented there is out-of-date. This website and the vixra.org versions are the only corrected and improved versions now available. Please note that there are very important refinements and applications that can be found at vixra.org. relative to such concepts as the ultra-logic-systems and the GGU-model schemes. Any article that contains the terms GGU-model, GD-model, GID-model and a few others listed at http://vixra.org/author/robert_a_herrmann should be consulted. The latest version of this book also appears, in three parts, at vixra.org )

The research presented in this book and the refinements recently made may be the most significant scientific work of my entire professional career. It was in Oct. 1978 when the concepts were first discovered that have produced the significant mathematical structure developed within the pages of this book. It began with the idea that it might be possible to model mathematically the concept known as subliminal perception and other similar notions that do not lend themselves to numerical modeling. The G-model, the D-world model, (the GD-model) the GGU-model, the MA-model the GID-model are five of the mathematical models obtained by application of these mathematical results. Information relative to these models can be found throughout these web pages. After many, many years of refinement, the methods that appear are, I believe, the simplest possible and are based upon a few human linguistic experiences that are practiced trillions of time a day within our earthly environment are modeled. The mathematical structure and processes were purposely chosen to be the simplest and least controversial. Indeed, to individuals who do research within nonstandard analysis these mathematical methods would be considered as very elementary in character. However, the intuitive interpretation and application of these methods my be difficult to grasp without considerable effort and reflection. As far as can be determined, there are no logical nor conceptual errors within this book. Typographical errors will not alter any specific result.

Einstein Corrected, (1995) (Nonstandard Analysis Applied to Special and General Relativity -The Theory of Infinitesimal Light-clocks.) Math. Dept U. S. Naval Academy, Annapolis, MD 21402-5002. (Some typographical corrections were made and this version may be a slight improvement over the one that appears at arxiv.org.)

The results presented here and in my published papers on this subject are not intended to denigrate those scientists who have, in the past, contributed to the Einstein theories or who continue to do so. It has been known for many years that the original Einstein method for deriving the physical behavior predicted by the Special Theory of Relativity and its later alteration, via the notation of an invariant property, yield an explicite contradiction and are unacceptable. Such an irrational contradiction can lead to disastrous consequences. Attempts have been made to correct this flaw, but each has failed. The corrections I have made are in the **foundations** for this theory and, hence, the General Theory as well. The fundamental "derivations" presented today yield the same contradiction. But, various results that do not depend upon such a contradiction are still valid. This implies that a non-contradictory completely rational derivation should exist. Such a derivation does exist and it is based upon the rather recently discovered rules for rigorous infinitesimal modeling.

Many unqualified individuals continue to present their own alternatives to these
Einstein theories, some claiming that the results are but an exercise in
high-school algebra. Further, many of these alternate theories ignore or contradict quantum physical descriptions for physical-system behavior. Certain scientific groups tend to categorize any and all criticisms of the Einstein theories as coming from the unqualified and lump such criticisms into the same unworthy category. However, many highly
qualified scientists of the past such as Builder, Fock, Ives and Dingle have
made such claims relative to the foundations of these two theories. For Ives
and Dingle, the fundamental approach was to assume that length
contraction, and not time dilation, is a real physical effect and it is this that leads
to the Einstein conclusions. In order to eliminate these
criticisms, Lawden states the "modern" interpretation is that length
contraction has no physical meaning, and only "time dilation" is of
significance. This modern assumption is certainly rather ad hoc in character.
*Further, theory "paradoxes" still appear within the literature and
are simply ignored by the scientific community.* There is, however, a reason
for this.

In 1992, the modified Special Theory derivation, which appears in most textbooks, was shown explicitly to contain additional logical error. Further, the original approach to Einstein's General Theory applies the same error and further utilizes a "geometric language," a language that has been criticized by many including John Wheeler as the incorrect approach to analyze the fundamental behavior of the universe in which we dwell. As Patton and Wheeler stated it,

". . . geometry is as far from giving an understanding of space as elasticity is from giving an understanding of a solid. . . . the basic structure is something deeper than geometry, that underlies both geometry and particles . . . what is the substance out of which the universe is made?"

Einstein used an explicit operational approach in his Special Theory, the "radar ranging" approach as we term it today. The basic error is that, for our universe, physical behavior does not rely merely upon "relative" behavior. There needs to be a "platform," so to speak, from which aspects of physical behavior are individually measured. Further, I respectfully submit that one of the greatest absurdities within modern science is that the concept of "time" is altered by physical behavior or physical entities as if "time" itself is a particle or field entity or the like. It is the measurement of this concept that is used to describe alterations in physical behavior. In this book, this absurdity has been eliminated by showing that one specific *measurement* of time is altered and, using this specific altered entity, all other appropriate behavioral alterations are predicted.

By using the modern corrected theory of the infinitesimal and infinite numbers as discovered by Robinson, all logical errors and "paradoxes" are removed. Moreover, using the correct rules for infinitesimal modeling various General Theory physical metrics are obtained without the need for tensor analysis and Riemannian geometry. One important aspect of this approach is that it does not in any manner contradict or eliminate any quantum physical theory. This new approach indirectly shows the existence of an additional interaction with a substratum composed of entities from the nonstandard physical world; a "world" that is distinct from what one defines as our physical world.

Some interesting results produced by this new investigation are (1) these theories are strongly related to "photon" properties and from these all other Special Theory properties are derived. (2) All alterations in physical-system behavior rigorously predicted by these theories would indirectly indicate an interaction is taking place with the "Nonstandard Photon-Particle Medium" (NSPPM). (3) The non-rigorous methods used to establish the universal constancy of a "speed for electromagnetic informational transmissions" need not hold unless a specific rigorous derivation, not using the "observer" notion, is applied. Relative to the General Grand Unification (GGU) Model, any verified Special Theory prediction is indirect evidence that each hyper-universe-wide frozen-frame (*UWFF) does contain the described NSPPM, which is a very special physical-like system. Indeed, this is remarkably strong indirect evidence for the existence of such a physical-like system, where the actual interaction of our physical world with the NSPPM cannot be directly observed from any physical-system. (Note: The most fundamental entities used within quantum physics also cannot be directly observed.)