Descriptive set theory and definable forcing:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2004
|
| Series: | Memoirs of the American Mathematical Society
793 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 167, number 793 (third of 5 numbers)." Includes bibliographical references |
| Physical Description: | VII, 141 S. |
| ISBN: | 0821834509 |
Staff View
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| 100 | 1 | |a Zapletal, Jindřich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Descriptive set theory and definable forcing |c Jindřich Zapletal |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2004 | |
| 300 | |a VII, 141 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 793 | |
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| 500 | |a Includes bibliographical references | ||
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| 650 | 4 | |a Continuum hypothesis | |
| 650 | 4 | |a Descriptive set theory | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 The subject of the book 1
1.2 The structure of the book 2
1.3 History and acknowledgments 3
1.4 Notation and literature 4
2 Definable forcing adding a single real 5
2.1 The factor algebras 5
2.2 Basic descriptive set theoretic considerations 9
2.3 Examples 14
2.3.1 The ideal of countable sets 15
2.3.2 The ideal of d bounded sets 15
2.3.3 The ideal of meager sets 16
2.3.4 The cmin ideal 16
2.3.5 Ideals generated by closed sets 19
2.3.6 The Laver ideal 21
2.3.7 Ideals associated with creature forcings 22
2.3.8 The Lebesgue null ideal 24
2.3.9 Mathias forcing 24
2.3.10 The Eo ideal 25
2.3.11 Silver forcing 29
2.3.12 The tx porous ideal 31
2.3.13 Steprans forcing 33
2.3.14 Hausdorff measures 37
2.3.15 Unions of ideals 41
2.3.16 Cross products of ideals 42
2.3.17 The cr splitting ideal 45
2.3.18 Namba forcing 45
3 The countable support iteration 47
3.1 A topological view of the iteration 47
3.2 The iterated Fubini powers of an ideal 52
3.3 A dichotomy for H on Sj ideals 55
3.4 A dichotomy for almost full ideals 58
v
vi CONTENTS
3.5 Other dichotomies 62
3.6 Cardinal invariants of the iterated ideals 66
4 Other forcings 71
4.1 Illfounded iterations 71
4.1.1 Strongly proper forcings 72
4.1.2 The ideals associated with countable length iterations . . 74
4.1.3 The properties of the factor ordering 77
4.1.4 The uncountable length 80
4.1.5 Sacks forcing iteration 81
4.2 Towers of ideals 82
4.2.1 Shooting a club with no infinite subset in the ground model 84
4.2.2 Shooting a club with finite intersection with every ground
model ordertype w set 86
5 Applications 91
5.1 Ciesielski Pawlikowski Axiom CPA and variations 91
5.1.1 The axioms 91
5.1.2 Absoluteness with no large cardinals 94
5.1.3 Absoluteness with large cardinals 97
5.2 Duality theorems 100
5.3 Interpolation theorems 102
5.4 Preservation theorems 106
5.4.1 Ergodic ideals 106
5.4.2 Preservation and ergodicity 109
5.4.3 Uniformity of a ideal generated by closed sets 114
A Examples of cardinal invariants 117
B The syntax of cardinal invariants 119
B.I The covering numbers 119
B.2 The tame and very tame invariants 123
C Effective descriptive set theory 125
D Large cardinals 133
D.I The absoluteness results 134
D.2 The determinacy results 134
|
| any_adam_object | 1 |
| author | Zapletal, Jindřich |
| author_facet | Zapletal, Jindřich |
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| dewey-full | 511.322 511.3/22 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 511.322 511.3/22 510 |
| dewey-search | 511.322 511.3/22 510 |
| dewey-sort | 3511.322 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV017536822 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:19:05Z |
| institution | BVB |
| isbn | 0821834509 |
| language | English |
| lccn | 2003061938 |
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| physical | VII, 141 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Zapletal, Jindřich Verfasser aut Descriptive set theory and definable forcing Jindřich Zapletal Providence, RI American Mathematical Society 2004 VII, 141 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 793 "Volume 167, number 793 (third of 5 numbers)." Includes bibliographical references Borelverzamelingen gtt Forcing (modeltheorie) gtt Lógica matemática larpcal Teoria descritiva dos conjuntos larpcal Verzamelingen (wiskunde) gtt Borel sets Continuum hypothesis Descriptive set theory Forcing (Model theory) Forcing (DE-588)4154978-8 gnd rswk-swf Deskriptive Mengenlehre (DE-588)4149180-4 gnd rswk-swf Kontinuumshypothese (DE-588)4481570-0 gnd rswk-swf Deskriptive Mengenlehre (DE-588)4149180-4 s DE-604 Forcing (DE-588)4154978-8 s Kontinuumshypothese (DE-588)4481570-0 s b DE-604 Memoirs of the American Mathematical Society 793 (DE-604)BV008000141 793 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zapletal, Jindřich Descriptive set theory and definable forcing Memoirs of the American Mathematical Society Borelverzamelingen gtt Forcing (modeltheorie) gtt Lógica matemática larpcal Teoria descritiva dos conjuntos larpcal Verzamelingen (wiskunde) gtt Borel sets Continuum hypothesis Descriptive set theory Forcing (Model theory) Forcing (DE-588)4154978-8 gnd Deskriptive Mengenlehre (DE-588)4149180-4 gnd Kontinuumshypothese (DE-588)4481570-0 gnd |
| subject_GND | (DE-588)4154978-8 (DE-588)4149180-4 (DE-588)4481570-0 |
| title | Descriptive set theory and definable forcing |
| title_auth | Descriptive set theory and definable forcing |
| title_exact_search | Descriptive set theory and definable forcing |
| title_full | Descriptive set theory and definable forcing Jindřich Zapletal |
| title_fullStr | Descriptive set theory and definable forcing Jindřich Zapletal |
| title_full_unstemmed | Descriptive set theory and definable forcing Jindřich Zapletal |
| title_short | Descriptive set theory and definable forcing |
| title_sort | descriptive set theory and definable forcing |
| topic | Borelverzamelingen gtt Forcing (modeltheorie) gtt Lógica matemática larpcal Teoria descritiva dos conjuntos larpcal Verzamelingen (wiskunde) gtt Borel sets Continuum hypothesis Descriptive set theory Forcing (Model theory) Forcing (DE-588)4154978-8 gnd Deskriptive Mengenlehre (DE-588)4149180-4 gnd Kontinuumshypothese (DE-588)4481570-0 gnd |
| topic_facet | Borelverzamelingen Forcing (modeltheorie) Lógica matemática Teoria descritiva dos conjuntos Verzamelingen (wiskunde) Borel sets Continuum hypothesis Descriptive set theory Forcing (Model theory) Forcing Deskriptive Mengenlehre Kontinuumshypothese |
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| volume_link | (DE-604)BV008000141 |
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