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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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©2009.
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | Perspectives in logic.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | "Association for Symbolic Logic." |
| Beschreibung: | 1 online resource (xvi, 444 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 409-424) and index. |
| ISBN: | 9780511580680 0511580681 9780511579110 051157911X |
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| author | Simpson, Stephen G. (Stephen George), 1945- |
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| author_corporate | Association for Symbolic Logic |
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| 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 |
| ctrlnum | (OCoLC)435767669 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
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| discipline | Mathematik |
| edition | 2nd ed. |
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| series2 | Perspectives in logic |
| spelling | Simpson, Stephen G. (Stephen George), 1945- https://id.oclc.org/worldcat/entity/E39PBJxRypbYYxyT4BCrjjwt8C http://id.loc.gov/authorities/names/n85298999 Subsystems of second order arithmetic / Stephen G. Simpson. 2nd ed. Cambridge ; New York : Cambridge University Press, ©2009. 1 online resource (xvi, 444 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Perspectives in logic "Association for Symbolic Logic." Includes bibliographical references (pages 409-424) and index. Print version record. 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. 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 Predicate calculus. http://id.loc.gov/authorities/subjects/sh85106251 Calcul des prédicats. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Predicate calculus fast Electronic books. Association for Symbolic Logic. http://id.loc.gov/authorities/names/n50054564 Print version: Simpson, Stephen G. (Stephen George), 1945- Subsystems of second order arithmetic. 2nd ed. Cambridge ; New York : Cambridge University Press, 2009 9780521884396 (DLC) 2008052364 (OCoLC)288374692 Perspectives in logic. http://id.loc.gov/authorities/names/no2009092095 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=284320 Volltext |
| spellingShingle | Simpson, Stephen G. (Stephen George), 1945- Subsystems of second order arithmetic / Perspectives in logic. 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 Predicate calculus. http://id.loc.gov/authorities/subjects/sh85106251 Calcul des prédicats. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Predicate calculus fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85106251 |
| title | Subsystems of second order arithmetic / |
| title_auth | Subsystems of second order arithmetic / |
| title_exact_search | Subsystems of second order arithmetic / |
| title_full | Subsystems of second order arithmetic / Stephen G. Simpson. |
| title_fullStr | Subsystems of second order arithmetic / Stephen G. Simpson. |
| title_full_unstemmed | Subsystems of second order arithmetic / Stephen G. Simpson. |
| title_short | Subsystems of second order arithmetic / |
| title_sort | subsystems of second order arithmetic |
| topic | Predicate calculus. http://id.loc.gov/authorities/subjects/sh85106251 Calcul des prédicats. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Predicate calculus fast |
| topic_facet | Predicate calculus. Calcul des prédicats. MATHEMATICS Infinity. MATHEMATICS Logic. Predicate calculus Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=284320 |
| work_keys_str_mv | AT simpsonstepheng subsystemsofsecondorderarithmetic AT associationforsymboliclogic subsystemsofsecondorderarithmetic |