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This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Book Synopsis Subsystems of Second Order Arithmetic by : Stephen George Simpson
Download or read book Subsystems of Second Order Arithmetic written by Stephen George Simpson and published by Cambridge University Press. This book was released on 2009-05-29 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
An original contribution to the foundations of mathematics, with emphasis on the role of set existence axioms, this book gives particular attention to several well known foundational programs including those by Hilbert, Bishop, and Weyl. The book includes an extensive bibliography and a detailed index, and should become a long-term standard reference in its field.
Book Synopsis Subsystems of Second Order Arithmetic by : Stephen G. Simpson
Download or read book Subsystems of Second Order Arithmetic written by Stephen G. Simpson and published by Springer. This book was released on 2012-01-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: An original contribution to the foundations of mathematics, with emphasis on the role of set existence axioms, this book gives particular attention to several well known foundational programs including those by Hilbert, Bishop, and Weyl. The book includes an extensive bibliography and a detailed index, and should become a long-term standard reference in its field.
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Book Synopsis Metamathematics of First-Order Arithmetic by : Petr Hájek
Download or read book Metamathematics of First-Order Arithmetic written by Petr Hájek and published by Cambridge University Press. This book was released on 2017-03-02 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics
Book Synopsis Slicing the Truth by : Denis R Hirschfeldt
Download or read book Slicing the Truth written by Denis R Hirschfeldt and published by World Scientific. This book was released on 2014-07-18 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics
Book Synopsis Proof-theoretic Investigations of Subsystems of Second-order Arithmetic by : Jeremy David Avigad
Download or read book Proof-theoretic Investigations of Subsystems of Second-order Arithmetic written by Jeremy David Avigad and published by . This book was released on 1995 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Subsystems of Second-order Arithmetic, and Descriptive Set Theory Under the Axiom of Determinateness by : Robert Alan Van Wesep
Download or read book Subsystems of Second-order Arithmetic, and Descriptive Set Theory Under the Axiom of Determinateness written by Robert Alan Van Wesep and published by . This book was released on 1977 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Book Synopsis Reverse Mathematics by : John Stillwell
Download or read book Reverse Mathematics written by John Stillwell and published by Princeton University Press. This book was released on 2019-09-24 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.
Book Synopsis Nonstandard Models of Arithmetic and Set Theory by : Ali Enayat
Download or read book Nonstandard Models of Arithmetic and Set Theory written by Ali Enayat and published by American Mathematical Soc.. This book was released on 2004 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Book Synopsis Handbook of Proof Theory by : S.R. Buss
Download or read book Handbook of Proof Theory written by S.R. Buss and published by Elsevier. This book was released on 1998-07-09 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.
Book Synopsis Mathematical Logic and Computation by : Jeremy Avigad
Download or read book Mathematical Logic and Computation written by Jeremy Avigad and published by . This book was released on 2022-09-12 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.
