Subsystems of Second Order Arithmetic
Edition: 2nd ed.
Series: Perspectives in Logic; Perspectives in Logic
Publisher: Cambridge University Press
Published: 2009
Place of publication: Leiden
Language: eng
Format: [electronic resource]
Number of pages: 462
ISBN-13: 9780511579851
Subjects: Predicate calculus
Description: Through a series of case studies, this volume examines these axioms to prove particular theorems in core mathematical areas.
Notes: Description based on print version record.
Table of contents: title: 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.; title: Chapter II RECURSIVE COMPREHENSIONChapter III ARITHMETICAL COMPREHENSION; Chapter IV WEAK KNIG'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.