Introduction to cardinal arithmetic:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1999
|
| Schriftenreihe: | Birkhäuser advanced texts : Basler Lehrbücher
Modern Birkhäuser classics |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 304 S. |
| ISBN: | 9783034603270 3764361247 0817661247 |
Internformat
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| 100 | 1 | |a Holz, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to cardinal arithmetic |c M. Holz ; K. Steffens ; E. Weitz |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1999 | |
| 300 | |a VI, 304 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Géométrie algébrique arithmétique |2 ram | |
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Datensatz im Suchindex
| _version_ | 1804127370699866112 |
|---|---|
| adam_text | Contents
Preface vii
Introduction 1
1 Foundations
1.1 The Axioms of ZFC 5
1.2 Ordinals 15
1.3 Transfinite Induction and Recursion 20
1.4 Arithmetic of Ordinals 30
1.5 Cardinal Numbers and their Elementary Properties 40
1.6 Infinite Sums and Products 58
1.7 Further Properties of kx the Singular Cardinal Hypothesis . . 70
1.8 Clubs and Stationary Sets 79
1.9 The Erdos Rado Partition Theorem 96
2 The Galvin Hajnal Theorem
2.1 Ideals and the Reduction of Relations 103
2.2 The Galvin Hajnal Formula 108
2.3 Applications of the Galvin Hajnal Formula 121
3 Ordinal Functions
3.1 Suprema and Cofinalities 131
3.2 K rapid Sequences and the Main Lemma of pcf Theory 143
3.3 The Definition and Simple Properties of pcf(a) 151
3.4 The Ideal J A(a) 159
4 Approximation Sequences
4.1 The Sets H(0) 173
4.2 Models and Absoluteness 176
4.3 Approximation Sequences 196
4.4 The Skolem Hull in H(9) 199
4.5 O Club Sequences 202
vi Contents
5 Generators of »T a+ (a)
5.1 Universal Sequences 209
5.2 The Existence of Generators 213
5.3 Properties of Generators 218
6 The Supremum of pcfM (a)
6.1 Control Functions 221
6.2 The Supremum of pcf/i(a) 225
7 Local Properties
7.1 The Ideals «7,(b) and J|A(a) 233
7.2 Intervals in pcf(a) 244
8 Applications of pcf Theory
8.1 Cardinal Estimates 249
8.2 Jonsson Algebras 251
8.3 A Partition Theorem of Todorcevic 262
8.4 Cofinalities of Partial Orderings ([A]^K,C) 265
9 The Cardinal Function pp(A)
9.1 pp(A) and the Theorems of Galvin, Hajnal and Silver 270
9.2 The Lemma of Galvin and Hajnal for pp(A) 275
Bibliography 287
List of Symbols 289
Index 293
|
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| dewey-ones | 511 - General principles of mathematics |
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| discipline | Mathematik Philosophie |
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| id | DE-604.BV012707687 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:16Z |
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| isbn | 9783034603270 3764361247 0817661247 |
| language | English |
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| physical | VI, 304 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Birkhäuser |
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| series2 | Birkhäuser advanced texts : Basler Lehrbücher Modern Birkhäuser classics |
| spelling | Holz, Michael Verfasser aut Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz Basel [u.a.] Birkhäuser 1999 VI, 304 S. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts : Basler Lehrbücher Modern Birkhäuser classics Arithmétique ram Géométrie algébrique arithmétique ram Cardinal numbers Kardinalzahl (DE-588)4163318-0 gnd rswk-swf Kardinalzahl (DE-588)4163318-0 s DE-604 Steffens, Karsten Verfasser aut Weitz, Edmund 1965- Verfasser (DE-588)116625559X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008638183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holz, Michael Steffens, Karsten Weitz, Edmund 1965- Introduction to cardinal arithmetic Arithmétique ram Géométrie algébrique arithmétique ram Cardinal numbers Kardinalzahl (DE-588)4163318-0 gnd |
| subject_GND | (DE-588)4163318-0 |
| title | Introduction to cardinal arithmetic |
| title_auth | Introduction to cardinal arithmetic |
| title_exact_search | Introduction to cardinal arithmetic |
| title_full | Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz |
| title_fullStr | Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz |
| title_full_unstemmed | Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz |
| title_short | Introduction to cardinal arithmetic |
| title_sort | introduction to cardinal arithmetic |
| topic | Arithmétique ram Géométrie algébrique arithmétique ram Cardinal numbers Kardinalzahl (DE-588)4163318-0 gnd |
| topic_facet | Arithmétique Géométrie algébrique arithmétique Cardinal numbers Kardinalzahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008638183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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