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 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 : Petr Hajek
language : en
Publisher: Springer
Release Date : 1993

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 1993 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.

Hilary Putnam On Logic And Mathematics

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Author : Geoffrey Hellman
language : en
Publisher: Springer
Release Date : 2018-12-06

Hilary Putnam On Logic And Mathematics written by Geoffrey Hellman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-06 with Mathematics categories.

This book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam’s work. It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy of mathematics. In addition, it features a short essay presenting reminiscences and anecdotes about Putnam from his friends and colleagues, and also includes an extensive bibliography of his work in mathematics and logic. The book offers readers a comprehensive review of outstanding contributions in logic and mathematics as well as an engaging dialogue between prominent scholars and researchers. It provides those interested in mathematical logic, the philosophy of logic, and the philosophy of mathematics unique insights into the work of Hilary Putnam.

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.

Theorem Proving With Analytic Tableaux And Related Methods

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Author : Peter Baumgartner
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-04-26

Theorem Proving With Analytic Tableaux And Related Methods written by Peter Baumgartner 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 1995-04-26 with Computers categories.

This volume constitutes the proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, TABLEAU '95, held at Schloß Rheinfels, St. Goar, Germany in May 1995. Originally tableau calculi and their relatives were favored primarily as a pedagogical device because of their advantages at the presentation level. The 23 full revised papers in this book bear witness that these methods have now gained fundamental importance in theorem proving, particularly as competitors for resolution methods. The book is organized in sections on extensions, modal logic, intuitionistic logic, the connection method and model elimination, non-clausal proof procedures, linear logic, higher-order logic, and applications

What Is Mathematics Really

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Author : Reuben Hersh
language : en
Publisher: Oxford University Press
Release Date : 1997-08-21

What Is Mathematics Really written by Reuben Hersh 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 1997-08-21 with Mathematics categories.

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Logic Colloquium 99

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Author : Jan Van Eijck
language : en
Publisher: CRC Press
Release Date : 2004-07-08

Logic Colloquium 99 written by Jan Van Eijck and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-08 with Mathematics categories.

A compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active are

Petr H Jek On Mathematical Fuzzy Logic

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Author : Franco Montagna
language : en
Publisher: Springer
Release Date : 2014-09-23

Petr H Jek On Mathematical Fuzzy Logic written by Franco Montagna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Mathematics categories.

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

Introduction To Mathematical Logic Fourth Edition

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Author : Elliott Mendelson
language : en
Publisher: CRC Press
Release Date : 1997-06-01

Introduction To Mathematical Logic Fourth Edition written by Elliott Mendelson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-01 with Mathematics categories.

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.