Subsystems of second order arithmetic / Stephen G. Simpson.

Format:

Book

Author/Creator:

Simpson, Stephen G. (Stephen George), 1945- author.

Contributor:

Association for Symbolic Logic, issuing body.

Series:

Perspectives in logic.

Perspectives in logic

Language:

English

Subjects (All):

Predicate calculus.

Physical Description:

1 online resource (xvi, 444 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2009.

Language Note:

English

Summary:

Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.

Contents:

COVER; HALF-TITLE; SERIES-TITLE; TITLE; COPYRIGHT; CONTENTS; LIST OF TABLES; PREFACE; ACKNOWLEDGMENTS; Chapter I INTRODUCTION; I.1. The Main Question; I.2. Subsystems of Z2; I.3. The System ACA0; I.4. Mathematics within ACA0; I.5. Pi11 -CA0 and Stronger Systems; I.6. Mathematics within Pi11 -CA0; I.7. The System RCA0; I.8. Mathematics within RCA0; I.9. Reverse Mathematics; I.10. The System WKL0; I.11. The System ATR0; I.12. The Main Question, Revisited; I.13. Outline of Chapters II through X; I.14. Conclusions; Part A DEVELOPMENT OF MATHEMATICS WITHIN SUBSYSTEMS OF Z2

Chapter II RECURSIVE COMPREHENSIONChapter III ARITHMETICAL COMPREHENSION; Chapter IV WEAK KÖNIG'S LEMMA; Chapter V ARITHMETICAL TRANSFINITE RECURSION; Chapter VI Pi11 COMPREHENSION; Part B MODELS OF SUBSYSTEMS OF Z2; Chapter VII beta-MODELS; Chapter VIII omega-MODELS; Chapter IX NON-omega-MODELS; APPENDIX; Chapter X ADDITIONAL RESULTS; BIBLIOGRAPHY; INDEX

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-20036-9

1-282-30296-5

9786612302961

0-511-58036-3

0-511-58068-1

0-511-57911-X

0-511-57837-7

0-511-58100-9

0-511-57985-3

OCLC:

609843112