Introduction to Ramsey spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
2010
|
| Series: | Annals of mathematics studies
174 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 287 S. |
| ISBN: | 9780691145419 9780691145426 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804143146583457792 |
|---|---|
| adam_text | Contents
Introduction
1
Chapter
1.
Ramsey Theory: Preliminaries
3
1.1
Coideals
3
1.2
Dimensions in Ramsey Theory
5
1.3
Higher Dimensions in Ramsey Theory
10
1.4
Ramsey Property and Baire Property
20
Chapter
2.
Semigroup Colorings
27
2.1
Idempotents in Compact semigroups
27
2.2
The Galvin-Glazer Theorem
30
2.3
Gowers s Theorem
34
2.4
A Semigroup of Subsymmetric
Ultrafilters
38
2.5
The Hales-Jewett Theorem
41
2.6
Partial Semigroup of Located Words
46
Chapter
3.
Trees and Products
49
3.1
Versions of the
Halpern-Läuchli
Theorem
49
3.2
A Proof of the
Halpern-Läuchli
Theorem
55
3.3
Products of Finite Sets
57
Chapter
4.
Abstract Ramsey Theory
63
4.1
Abstract Baire Property
63
4.2
The Abstract Ramsey Theorem
68
4.3
Combinatorial Forcing
76
4.4
The Hales-Jewett Space
83
4.5
Ramsey Spaces of Infinite Block Sequences of Located Words
89
Chapter
5.
Topological Ramsey Theory
93
5.1
Topological Ramsey Spaces
93
5.2
Topological Ramsey Spaces of Infinite Block Sequences of Vectors
99
5.3
Topological Ramsey Spaces of Infinite
Sequences of Variable Words
105
5.4
Parametrized Versions of
Rosenthal
Dichotomies 111
5.5
Ramsey Theory of Superperfect Subsets of Polish Spaces
117
5.6
Dual Ramsey Theory
121
vi
CONTENTS
5.7
A
Ramsey Space of Infinite-Dimensional
Vector Subspaces of FN
127
Chapter
6.
Spaces of Trees
135
6.1
A Ramsey Space of Strong Subtrees
135
6.2
Applications of the Ramsey Space of Strong Subtrees
138
6.3
Partition Calculus on Finite Powers of the Countable Dense Lin¬
ear Ordering
143
6.4
A Ramsey Space of Increasing Sequences of Rationale
149
6.5
Continuous Colorings on Q1*1
152
6.6
Some Perfect Set Theorems
158
6.7
Analytic Ideals and Points in Compact Sets of the First Baire Class
165
Chapter
7.
Local Ramsey Theory
179
7.1
Local Ellentuck Theory
179
7.2
Topological Ultra-Ramsey Spaces
190
7.3
Some Examples of Selective Coideals on
N 194
7.4
Some Applications of Ultra-Ramsey Theory
198
7.5
Local Ramsey Theory and Analytic
Topologies on
N 202
7.6
Ultra-Hales-Jewett Spaces
207
7.7
Ultra-Ramsey Spaces of Block Sequences of Located Words
212
7.8
Ultra-Ramsey Space of Infinite
Block Sequences of Vectors
215
Chapter
8.
Infinite Products of Finite Sets
219
8.1
Semicontinuous Colorings of Infinite
Products of Finite Sets
219
8.2
Polarized Ramsey Property
224
8.3
Polarized Partition Calculus
231
Chapter
9.
Parametrized Ramsey Theory
237
9.1
Higher Dimensional Ramsey Theorems
Parametrized by Infinite Products of Finite Sets
237
9.2
Combinatorial Forcing Parametrized by
Infinite Products of Finite Sets
243
9.3
Parametrized Ramsey Property
248
9.4
Infinite-Dimensional Ramsey Theorem
Parametrized by Infinite Products of Finite Sets
254
Appendix
259
Bibliography
271
Subject Index
279
Index of Notation
285
|
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| indexdate | 2024-07-09T22:43:01Z |
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| isbn | 9780691145419 9780691145426 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020487855 |
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| physical | VI, 287 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Princeton Univ. Press |
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| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Todorcevic, Stevo 1965- Verfasser (DE-588)115235620 aut Introduction to Ramsey spaces Stevo Todorcevic Princeton, NJ Princeton Univ. Press 2010 VI, 287 S. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 174 Ramsey-Theorie (DE-588)4212682-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Ramsey-Theorie (DE-588)4212682-4 s DE-604 Annals of mathematics studies 174 (DE-604)BV000000991 174 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020487855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Todorcevic, Stevo 1965- Introduction to Ramsey spaces Annals of mathematics studies Ramsey-Theorie (DE-588)4212682-4 gnd |
| subject_GND | (DE-588)4212682-4 (DE-588)4123623-3 |
| title | Introduction to Ramsey spaces |
| title_auth | Introduction to Ramsey spaces |
| title_exact_search | Introduction to Ramsey spaces |
| title_full | Introduction to Ramsey spaces Stevo Todorcevic |
| title_fullStr | Introduction to Ramsey spaces Stevo Todorcevic |
| title_full_unstemmed | Introduction to Ramsey spaces Stevo Todorcevic |
| title_short | Introduction to Ramsey spaces |
| title_sort | introduction to ramsey spaces |
| topic | Ramsey-Theorie (DE-588)4212682-4 gnd |
| topic_facet | Ramsey-Theorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020487855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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