Metamathematics Of First Order Arithmetic
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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 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.
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).
Metamathematics Of First Order Arithmetic
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Author : Petr Hajek
language : en
Publisher: Springer
Release Date : 1998-03-17
Metamathematics Of First Order Arithmetic written by Petr Hajek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-17 with Mathematics categories.
People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The aim of the book by Hajek and Pudlak is to cover some of the most important results in the study of a first order theory of the natural numbers, called Peano arithmetic and its fragments (subtheories). The field is quite active, but only a small part of the results has been covered in monographs. This book is divided into three parts. In Part A, the authors develop parts of mathematics and logic in various fragments. Part B is devoted to incompleteness. Part C studies systems that have the induction schema restricted to bounded formulas (Bounded Arithmetic). One highlight of this section is the relation of provability to computational complexity. The study of formal systems for arithmetic is a prerequisite for understanding results such as Gödel's theorems. This book is intended for those who want to learn more about such systems and who want to follow current research in the field. The book contains a bibliography of approximately 1000 items.
Metamathematics Of First Order Arithmetic
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Author : P Hajek
language : en
Publisher:
Release Date : 1998
Metamathematics Of First Order Arithmetic written by P Hajek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Introduction To Metamathematics
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Author : Stephen Cole Kleene
language : en
Publisher:
Release Date : 1971
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 1971 with Functions categories.
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.
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.
Proof Theory
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Author : Gaisi Takeuti
language : en
Publisher: Courier Corporation
Release Date : 2013-10-10
Proof Theory written by Gaisi Takeuti and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-10 with Mathematics categories.
This comprehensive monograph presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.
A Beginner S Guide To Mathematical Logic
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Author : Raymond M. Smullyan
language : en
Publisher: Courier Corporation
Release Date : 2014-03-19
A Beginner S Guide To Mathematical Logic written by Raymond M. Smullyan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-19 with Mathematics categories.
Combining stories of great writers and philosophers with quotations and riddles, this completely original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2013 edition.