Descriptive set theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2009]
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| Edition: | Second edition |
| Series: | Mathematical surveys and monographs
Volume 155 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 502 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821848135 |
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| adam_text | Titel: Descriptive set theory
Autor: Moschovakis, Yiannis N
Jahr: 2009
Mathematical Surveys and Monographs Volume 155 Descriptive Set Theory Second Edition Yiannis N. Moschovakis ^VDF.D American Mathematical Society Providence, Rhode Island
CONTENTS Preface to the second edition ............................................... ix Preface to the first edition ................................................. xi About this book ............................................................ xiii Introduction............................................................... 1 Chapter 1. The basic classical notions.................................... 9 IA. Perfect Polish spaces.............................................. 9 IB. The Borel pointclasses of finite order............................... 13 IC. Computing with relations; closure properties....................... 18 ID. Parametrization and hierarchy theorems............................ 26 IE. The projective sets................................................ 29 IF. Countable operations............................................ 33 IG. Borel functions and isomorphisms................................. 37 IH. Historical and other remarks...................................... 46 Chapter 2. a-Suslin and 2-Borel.......................................... 49 2A. The Cantor-Bendixson Theorem................................... 50 2B. K-Suslin sets...................................................... 51 2C. Trees and the Perfect Set Theorem................................. 57 2D. Wellfounded trees................................................. 62 2E. The Suslin Theorem............................................... 65 2F. Inductive analysis of projections of trees............................ 70 2G. The Kunen-Martin Theorem...................................... 74 2H. Category and measure............................................. 79 21. Historical remarks................................................ 85 Chapter 3. Basic notions of the effective theory.......................... 87 3 A. Recursive functions on the integers................................. 89 3B. Recursive
presentations............................................ 96 3C. Semirecursive pointsets............................................101 3D. Recursive and T-recursive functions................................110 3E. The Kleene pointclasses...........................................118 3F. Universal sets for the Kleene pointclasses...........................125 3G. Partial functions and the substitution property..................... 130 3H. Codings, uniformity and good parametrizations....................135 31. Effective theory on arbitrary (perfect) Polish spaces.................141 VÜ
CONTENTS viii 3J. Historical remarks................................................142 Chapter 4. Structure theory for pointclasses............................145 4A. The basic representation theorem for n¡ sets....................... 145 4B. The prewellordering property......................................152 4C. Spector pointclasses...............................................158 4D. The parametrization theorem for A n X ............................165 4E. The uniformization theorem for nj, Ej.............................173 4F. Additional results about n¡ ....................................... 184 4G. Historical remarks................................................202 Chapter 5. The constructible universe....................................207 5A. Descriptive set theory in L .........................................208 5B. Independence results obtained by the method of forcing.............214 5C. Historical remarks................................................215 Chapter 6. The playful universe..........................................217 6A. Infinite games of perfect information...............................218 6B. The First Periodicity Theorem.....................................229 6C. The Second Periodicity Theorem; uniformization...................235 6D. The game quantifier D.............................................244 6E. The Third Periodicity Theorem....................................254 6F. The determinacy of Borel sets.....................................272 6G. Measurable cardinals..............................................280 6H. Historical remarks................................................290 Chapter 7. The recursion theorem........................................293 7A. Recursion in a E*-pointclass.......................................293 7B. The Suslin-Kleene Theorem.......................................298 7C. Inductive
definability..............................................309 7D. The completely playful universe....................................323 7E. Historical remarks................................................339 7F Results which depend on the Axiom of Choice......................341 Chapter 8. Metamathematics..............................................353 8A. Structures and languages..........................................355 8B. Elementary definability............................................365 8C. Definability in the universe of sets..................................371 8D. Godel’s universe of constructible sets...............................381 8E. Absoluteness.....................................................390 8F The basic facts about L ............................................401 8G. Regularity results and inner models................................416 8H. On the theory of indiscernibles .....................................446 81. Some remarks about strong hypotheses.............................468 8J. Historical remarks................................................473 The axiomatics of pointclasses..............................................475 References..................................................................477 Index 491
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:36:58Z |
| institution | BVB |
| isbn | 9780821848135 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020182012 |
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| owner | DE-11 |
| owner_facet | DE-11 |
| physical | xiv, 502 Seiten Illustrationen, Diagramme |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Moschovakis, Yiannis N. 1938- Verfasser (DE-588)112687776 aut Descriptive set theory Yiannis N. Moschovakis Second edition Providence, Rhode Island American Mathematical Society [2009] © 2009 xiv, 502 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 155 Deskriptive Mengenlehre (DE-588)4149180-4 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Deskriptive Mengenlehre (DE-588)4149180-4 s DE-604 Mengenlehre (DE-588)4074715-3 s Erscheint auch als Online-Ausgabe 978-1-4704-1382-8 Mathematical surveys and monographs Volume 155 (DE-604)BV000018014 155 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020182012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moschovakis, Yiannis N. 1938- Descriptive set theory Mathematical surveys and monographs Deskriptive Mengenlehre (DE-588)4149180-4 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4149180-4 (DE-588)4074715-3 |
| title | Descriptive set theory |
| title_auth | Descriptive set theory |
| title_exact_search | Descriptive set theory |
| title_full | Descriptive set theory Yiannis N. Moschovakis |
| title_fullStr | Descriptive set theory Yiannis N. Moschovakis |
| title_full_unstemmed | Descriptive set theory Yiannis N. Moschovakis |
| title_short | Descriptive set theory |
| title_sort | descriptive set theory |
| topic | Deskriptive Mengenlehre (DE-588)4149180-4 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Deskriptive Mengenlehre Mengenlehre |
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