Classical descriptive set theory
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and...
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
New York, NY
Springer-Verlag
1995
Springer New York |
| Edition | 1 |
| Series | Graduate Texts in Mathematics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 1461286921 9783540943747 9781461286929 9780387943749 0387943749 3540943749 9781461241911 146124191X |
| ISSN | 0072-5285 |
| DOI | 10.1007/978-1-4612-4190-4 |
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| Abstract | Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation. |
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| AbstractList | Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation. |
| Author | Kechris, Alexander S. |
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| Copyright | Springer-Verlag New York 1995 |
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| DOI | 10.1007/978-1-4612-4190-4 |
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| Discipline | Mathematics |
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| ISSN | 0072-5285 |
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| Notes | Includes bibliographical references (p. [369]-380) and index "Softcover reprint of the hardcover 1st edition 1995"--T.p. verso of softcover |
| OCLC | 958524358 |
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| PublicationCentury | 1900 |
| PublicationDate | c1995 1995 1995. |
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| PublicationSeriesTitle | Graduate Texts in Mathematics |
| PublicationYear | 1995 |
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| Snippet | Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced... |
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| SubjectTerms | Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematics Mathematics and Statistics Set theory Topology |
| TableOfContents | Graduate Texts in Mathematics -- Classical Descriptive Set Theory -- Copyright -- Preface -- Contents -- Introduction -- About This Book -- CHAPTER I Polish Spaces -- CHAPTER II Borel Sets -- CHAPTER III Analytic Sets -- CHAPTER IV Co-Analytic Sets -- CHAPTER V Projective Sets -- Appendix A. Ordinals and Cardinals -- Appendix B. Well-founded Relations -- Appendix C. On Logical Notation -- Notes and Hints -- References -- Symbols and Abbreviations -- Index I Polish Spaces -- 1. Topological and Metric Spaces -- 2. Trees -- 3. Polish Spaces -- 4. Compact Metrizable Spaces -- 5. Locally Compact Spaces -- 6. Perfect Polish Spaces -- 7.Zero-dimensional Spaces -- 8. Baire Category -- 9. Polish Groups -- II Borel Sets -- 10. Measurable Spaces and Functions -- 11. Borel Sets and Functions -- 12. Standard Borel Spaces -- 13. Borel Sets as Clopen Sets -- 14. Analytic Sets and the Separation Theorem -- 15. Borel Injections and Isomorphisms -- 16. Borel Sets and Baire Category -- 17. Borel Sets and Measures -- 18. Uniformization Theorems -- 19. Partition Theorems -- 20. Borel Determinacy -- 21. Games People Play -- 22. The Borel Hierarchy -- 23. Some Examples -- 24. The Baire Hierarchy -- III Analytic Sets -- 25. Representations of Analytic Sets -- 26. Universal and Complete Sets -- 27. Examples -- 28. Separation Theorems -- 29. Regularity Properties -- 30. Capacities -- 31. Analytic Well-founded Relations -- IV Co-Analytic Sets -- 32. Review -- 33. Examples -- 34. Co-Analytic Ranks -- 35. Rank Theory -- 36. Scales and Uniformiiatiou -- V Projective Sets -- 37. The Projective Hierarchy -- 38. Projective Determinacy -- 39. The Periodicity Theorems -- 40. Epilogue -- Appendix A. Ordinals and Cardinals -- Appendix B. Well-founded Relations -- Appendix C. On Logical Notation -- Notes and Hints -- References -- Symbols and Abbreviations. |
| Title | Classical descriptive set theory |
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