UNDECIDABLE THEORIES STUDIES IN LOGIC AND THE FOUNDATION OF MATHEMATICS DOVER BOOKS ON MATHEMATICS

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## The Foundations of Computability Theory

Author: Borut Robič

Publisher: Springer

ISBN: 3662448084

Category: Computers

Page: 331

View: 3269

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.## On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Author: Kurt Gödel

Publisher: Courier Corporation

ISBN: 9780486669809

Category: Mathematics

Page: 72

View: 7582

In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.## Foundations of Radiation Hydrodynamics

Author: Dimitri Mihalas,Barbara Weibel Mihalas

Publisher: Courier Corporation

ISBN: 0486135888

Category: Science

Page: 752

View: 7015

Excellent, informative volume focuses on dynamics of nonradiating fluids, problems involving waves, shocks and stellar winds, physics of radiation, radiation transport, and the dynamics of radiating fluids. 1984 edition.## Logic for Computer Science

Author: Jean H. Gallier

Publisher: Courier Dover Publications

ISBN: 0486805085

Category: Mathematics

Page: 528

View: 5170

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.## An Introduction to the Theory of Elasticity

Author: R. J. Atkin,N. Fox

Publisher: Courier Corporation

ISBN: 0486150992

Category: Science

Page: 272

View: 501

Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.## Atomic Physics: 8th Edition

Author: Max Born

Publisher: Courier Corporation

ISBN: 0486318583

Category: Science

Page: 544

View: 8824

Nobel Laureate's lucid treatment of kinetic theory of gases, elementary particles, nuclear atom, wave-corpuscles, atomic structure and spectral lines, much more. Over 40 appendices, bibliography.## Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 2170

Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.## Non-Linear Elastic Deformations

Author: R. W. Ogden

Publisher: Courier Corporation

ISBN: 0486318710

Category: Technology & Engineering

Page: 544

View: 9485

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.## An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

View: 4584

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.## Mechanism, Mentalism and Metamathematics

Author: J. Webb

Publisher: Springer Science & Business Media

ISBN: 940157653X

Category: Philosophy

Page: 285

View: 2544

This book grew out of a graduate student paper [261] in which I set down some criticisms of J. R. Lucas' attempt to refute mechanism by means of G6del's theorem. I had made several such abortive attempts myself and had become familiar with their pitfalls, and especially with the double edged nature of incompleteness arguments. My original idea was to model the refutation of mechanism on the almost universally accepted G6delian refutation of Hilbert's formalism, but I kept getting stuck on questions of mathematical philosophy which I found myself having to beg. A thorough study of the foundational works of Hilbert and Bernays finally convinced me that I had all too naively and uncritically bought this refutation of formalism. I did indeed discover points of surprisingly close contact between formalism and mechanism, but also that it was possible to under mine certain strong arguments against these positions precisely by invok ing G6del's and related work. I also began to realize that the Church Turing thesis itself is the principal bastion protecting mechanism, and that G6del's work was perhaps the best thing that ever happened to both mechanism and formalism. I pushed these lines of argument in my dis sertation with the patient help of my readers, Raymond Nelson and Howard Stein. I would especially like to thank the latter for many valuable criticisms of my dissertation as well as some helpful suggestions for reor ganizing it in the direction of the present book.## Einführung in die Mathematische Logik

Author: Alfred Tarski

Publisher: Springer-Verlag

ISBN: 3709159288

Category: Mathematics

Page: 166

View: 8520

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.## Applied Nonstandard Analysis

Author: Martin Davis

Publisher: Courier Corporation

ISBN: 0486152340

Category: Mathematics

Page: 208

View: 2802

This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.