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Subsystems of second order arithmetic /

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 to...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Simpson, Stephen G. (Stephen George), 1945-
Autor Corporativo: Association for Symbolic Logic
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, ©2009.
Edición:2nd ed.
Colección:Perspectives in logic.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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