Cardinal arithmetic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1994
|
| Schriftenreihe: | Oxford logic guides
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXI, 481 S. |
| ISBN: | 0198537859 |
Internformat
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| 245 | 1 | 0 | |a Cardinal arithmetic |c Saharon Shelah |
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Datensatz im Suchindex
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| adam_text | CONTENTS
Contents vii
Acknowledgements x
Introduction xi
Basic definitions xvi
Annotated contents xvii
Modern history of cardinal arithmetic xxv
Could Cantor really have read it or what the reader
is assumed to know xxix
I Basic: cofinalities of small reduced products
[Sh 345a] 1
§0 Introduction 1
§1 The basic properties of pcf(a) 2
§2 Normality of A € pcf(a) for a 13
§3 Getting better representation: generating sequences
and cofinality systems 21
II Kw+i has a Jonsson algebra [Sh 355] 34
§0 Introduction 34
§1 Existence of lub in products, and representations of
A+ as true cofinality 40
§2 On pp instead of the Singular Cardinal Problem 54
§3 The cofinality of II a 60
§4 Applications 66
§5 Covering numbers, pp 84
§6 A Preeness 96
§7 Existence of Loo^ equivalent non isomorphic models
of singular cardinality A 108
III There are Jonsson algebras in many inacces¬
sible cardinals [Sh 365] 117
§0 Introduction 117
§1 Guessing clubs 118
§2 Finding C s which guess clubs _ 123
§3 Existence of Jonsson algebra and idp(C,I) 138
§4 Existence of strong colouring 156
IV Jonsson algebras in inaccessibles A, not A Mahlo
[Sh 380] 185
viii Contents
§0 Introduction 185
§1 The first A which is regular Jonsson is A Mahlo 185
§2 If A is inaccessible not A Mahlo then on A there is a
Jonsson algebra 196
V Bounding pp(//) when fi cf(/x) Ko using
ranks and normal filters [Sh 386] 213
§0 Introduction 213
§1 Existence of nice i s 221
§2 Various ranks 229
§3 More on ranks 239
§4 Preservative pairs 249
§5 Conclusions 259
VI Bounds on power of singulars: Induction [Sh 333]
266
§0 Introduction 266
§1 A generic ultrapower of the universe which has a A
like initial segment for almost every A 267
§2 The family of preservative pairs is closed under in¬
duction 269
VII Strong Covering Lemma and CH in V[r] [Sh g7]
275
§0 Introduction 275
§1 The Strong Covering Lemma: Definition and impli¬
cations 279
§2 Proof of the Strong Covering Lemma 284
§3 A counterexample 300
§4 When adding a real cannot destroy CH 302
VIII Advanced: Cofinalities of reduced products [Sh 371]
311
§0 Introduction 311
§1 Representation as true cofinality of products modulo
Jcbd 312
§2 J [a] is simply generated 327
§3 Also quite large b C pcf(a) behave nicely 333
§4 On prcj 341
§5 Successor of singular + ideal and A+ narrow order
B.A. in A+ 347
§6 npt and successor of regular 353
IX Cardinal Arithmetic [Sh 400] 358
§0 Introduction 358
Contents ix
§1 pp(A) = cov(A, A, Ni, 2) for the first non trivial A 362
§2 Why the HELL is it four? 371
§3 The smallest number of functions required to cover
all small products 376
§4 If 6 N4 has countable cofinality then ppN« N^ 388
§5 pp(A) large enough sufficient condition 398
Appendix
1 Colorings [Sh 282a] 416
2 Entangled orders and narrow Boolean alge¬
bras [Sh 345b] 424
Analytical Guide 435
Anotated content of continuations 461
References 471
|
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| id | DE-604.BV009998895 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:44:40Z |
| institution | BVB |
| isbn | 0198537859 |
| language | English |
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| oclc_num | 246784152 |
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| physical | XXXI, 481 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Shelah, Saharon 1945- Verfasser (DE-588)120062755 aut Cardinal arithmetic Saharon Shelah Oxford Clarendon Press 1994 XXXI, 481 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 29 Kardinalzahltheorie (DE-588)4163319-2 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Kardinalzahl (DE-588)4163318-0 gnd rswk-swf Kardinalzahltheorie (DE-588)4163319-2 s DE-604 Kardinalzahl (DE-588)4163318-0 s Arithmetik (DE-588)4002919-0 s DE-188 Oxford logic guides 29 (DE-604)BV000013997 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006628384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shelah, Saharon 1945- Cardinal arithmetic Oxford logic guides Kardinalzahltheorie (DE-588)4163319-2 gnd Arithmetik (DE-588)4002919-0 gnd Kardinalzahl (DE-588)4163318-0 gnd |
| subject_GND | (DE-588)4163319-2 (DE-588)4002919-0 (DE-588)4163318-0 |
| title | Cardinal arithmetic |
| title_auth | Cardinal arithmetic |
| title_exact_search | Cardinal arithmetic |
| title_full | Cardinal arithmetic Saharon Shelah |
| title_fullStr | Cardinal arithmetic Saharon Shelah |
| title_full_unstemmed | Cardinal arithmetic Saharon Shelah |
| title_short | Cardinal arithmetic |
| title_sort | cardinal arithmetic |
| topic | Kardinalzahltheorie (DE-588)4163319-2 gnd Arithmetik (DE-588)4002919-0 gnd Kardinalzahl (DE-588)4163318-0 gnd |
| topic_facet | Kardinalzahltheorie Arithmetik Kardinalzahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006628384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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