Recursion Theory For Metamathematics
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Recursion Theory For Metamathematics
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Author : Raymond M. Smullyan
language : en
Publisher:
Release Date : 2020
Recursion Theory For Metamathematics written by Raymond M. Smullyan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Recursion theory 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 text 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.
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.
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.
Diagonalization And Self Reference
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Author : Raymond M. Smullyan
language : en
Publisher: Oxford Logic Guides
Release Date : 1994
Diagonalization And Self Reference written by Raymond M. Smullyan and has been published by Oxford Logic Guides this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Language Arts & Disciplines categories.
The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The firstchapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.
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.
Metamath A Computer Language For Mathematical Proofs
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Author : Norman Megill
language : en
Publisher: Lulu.com
Release Date : 2019
Metamath A Computer Language For Mathematical Proofs written by Norman Megill and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Computers categories.
Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.
Inexhaustibility
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Author : Torkel Franzén
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30
Inexhaustibility written by Torkel Franzén 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 2017-03-30 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 sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.
Theory Of Formal Systems
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Author : Raymond M. Smullyan
language : en
Publisher: Princeton University Press
Release Date : 1961
Theory Of Formal Systems written by Raymond M. Smullyan and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Mathematics categories.
This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
Sets Models And Proofs
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Author : Ieke Moerdijk
language : en
Publisher: Springer
Release Date : 2018-11-23
Sets Models And Proofs written by Ieke Moerdijk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-23 with Mathematics categories.
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
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.