Recursive Functions And Metamathematics
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Recursive Functions And Metamathematics
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Author : Roman Murawski
language : en
Publisher:
Release Date : 2014-01-15
Recursive Functions And Metamathematics written by Roman Murawski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Recursive Functions And Metamathematics
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Author : Roman Murawski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Recursive Functions And Metamathematics written by Roman Murawski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Philosophy categories.
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.
Recursion Theory For Metamathematics
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Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1993-01-28
Recursion Theory For Metamathematics written by Raymond M. Smullyan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-28 with Mathematics categories.
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel'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.
Mechanism Mentalism And Metamathematics
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Author : J. Webb
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Mechanism Mentalism And Metamathematics written by J. Webb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
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.
An Early History Of Recursive Functions And Computability
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Author : Rod Adams
language : en
Publisher: Docent Press
Release Date : 2011
An Early History Of Recursive Functions And Computability written by Rod Adams and has been published by Docent Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Introduction To Metamathematics
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Author : Stephen Cole Kleene
language : en
Publisher:
Release Date : 1952
Introduction To Metamathematics written by Stephen Cole Kleene and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Mathematics categories.
Higher Recursion Theory
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Author : Gerald E. Sacks
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Higher Recursion Theory written by Gerald E. Sacks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Computers categories.
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Metamathematics Of First Order Arithmetic
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Author : Petr Hájek
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02
Metamathematics Of First Order Arithmetic written by Petr Hájek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Metamathematics Machines And G Del S Proof
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Author : N. Shankar
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-30
Metamathematics Machines And G Del S Proof written by N. Shankar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-30 with Computers categories.
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Notes For Lectures On Metamathematics Given At Stanford University 1961 1962
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Author : Solomon Feferman
language : en
Publisher:
Release Date : 1962
Notes For Lectures On Metamathematics Given At Stanford University 1961 1962 written by Solomon Feferman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Logic, Symbolic and mathematical categories.