Recursive Functions And Metamathematics

Author : Roman Murawski
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 41,7 Mb
Release : 2013-03-14
Category : Philosophy
ISBN : 9789401728669

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Recursive Functions and Metamathematics by Roman Murawski Pdf

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

Author : Roman Murawski
Publisher : Unknown
Page : 412 pages
File Size : 40,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401728674

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Recursive Functions and Metamathematics by Roman Murawski Pdf

Author : Raymond M. Smullyan
Publisher : Oxford University Press on Demand
Page : 180 pages
File Size : 55,5 Mb
Release : 1993
Category : Social Science
ISBN : 9780195082326

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Recursion Theory for Metamathematics by Raymond M. Smullyan Pdf

This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Author : Hartley Rogers
Publisher : Unknown
Page : 526 pages
File Size : 55,6 Mb
Release : 1967
Category : Mathematics
ISBN : UOM:39015013841039

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Theory of Recursive Functions and Effective Computability by Hartley Rogers Pdf

Author : Stephen Cole Kleene,Richard Eugene Vesley
Publisher : Unknown
Page : 222 pages
File Size : 47,5 Mb
Release : 1965
Category : Intuitionistic mathematics
ISBN : UOM:39015068271272

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The Foundations of Intuitionistic Mathematics by Stephen Cole Kleene,Richard Eugene Vesley Pdf

Author : Petr Hájek,Pavel Pudlák
Publisher : Cambridge University Press
Page : 475 pages
File Size : 55,8 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168411

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Metamathematics of First-Order Arithmetic by Petr Hájek,Pavel Pudlák Pdf

A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

Author : Stephen Cole Kleene
Publisher : Unknown
Page : 572 pages
File Size : 50,7 Mb
Release : 1952
Category : Mathematics
ISBN : UCBK:C048029916

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Introduction to Metamathematics by Stephen Cole Kleene Pdf

Author : S.C. Kleene
Publisher : North Holland
Page : 0 pages
File Size : 42,6 Mb
Release : 1980-01-01
Category : Computers
ISBN : 0720421039

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Introduction to Metamathematics by S.C. Kleene Pdf

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gadel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which nothing was ever the same. Kleene was an important figure in logic, and lived a long full life of scholarship and teaching. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gade1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Gadel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.

Author : Klaus Ambos-Spies,Gert H. Müller,Gerald E. Sacks
Publisher : Springer
Page : 398 pages
File Size : 47,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540471424

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Recursion Theory Week by Klaus Ambos-Spies,Gert H. Müller,Gerald E. Sacks Pdf

These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.

Author : Lev D. Beklemishev
Publisher : Elsevier
Page : 189 pages
File Size : 44,6 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080957404

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Provability, Computability and Reflection by Lev D. Beklemishev Pdf

Studies in Logic publishes monographs and occasionally edited volumes in the area of mathematical logic and its applications.

Author : Ljubomir Lalov Ivanov
Publisher : Unknown
Page : 268 pages
File Size : 48,6 Mb
Release : 1986
Category : Recursion theory
ISBN : UCAL:B4502352

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Algebraic Recursion Theory by Ljubomir Lalov Ivanov Pdf

Author : Rod Adams
Publisher : Docent Press
Page : 312 pages
File Size : 44,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780983700401

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An Early History of Recursive Functions and Computability by Rod Adams Pdf

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

Author : Hans Hermes
Publisher : Springer
Page : 255 pages
File Size : 54,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662116869

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Enumerability, Decidability, Computability by Hans Hermes Pdf

The task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success.

Author : Stephen Cole Kleene
Publisher : Unknown
Page : 560 pages
File Size : 40,5 Mb
Release : 2012-07-01
Category : Electronic
ISBN : 1258442469

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Introduction to Metamathematics by Stephen Cole Kleene Pdf

Author : René Cori,Daniel Lascar
Publisher : Oxford University Press, USA
Page : 360 pages
File Size : 55,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0198500513

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Mathematical Logic by René Cori,Daniel Lascar Pdf

Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course, . It is a major element in theoretical computer sciences and has undergone a huge revival with the growing importance of computer science. This text is based on a course for undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence while still covering a wide area of logic. It starts with recursion theory and follows Godel's incompleteness theorems and axiomatic set theory as well as an introduction to model theory. There are examples throughout each section and a varied selection of exercises at the end with answers given in the appendix