Walks on ordinals and their characteristics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2007
|
| Series: | Progress in mathematics
Volume 263 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 324 Seiten Diagramme |
| ISBN: | 9783764385286 3764385286 |
Staff View
MARC
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| 100 | 1 | |a Todorcevic, Stevo |d 1965- |e Verfasser |0 (DE-588)115235620 |4 aut | |
| 245 | 1 | 0 | |a Walks on ordinals and their characteristics |c Stevo Todorcevic |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2007 | |
| 300 | |a VI, 324 Seiten |b Diagramme | ||
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| 490 | 1 | |a Progress in mathematics |v Volume 263 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction
1.1 Walks and the metric theory of ordinals 1
1.2 Summary of results 10
1.3 Prerequisites and notation 17
1.4 Acknowledgements 18
2 Walks on Countable Ordinals
2.1 Walks on countable ordinals and their basic characteristics 19
2.2 The coherence of maximal weights 29
2.3 Oscillations of traces 40
2.4 The number of steps and the last step functions 47
3 Metric Theory of Countable Ordinals
3.1 Triangle inequalities 55
3.2 Constructing a Souslin tree using p 58
3.3 A Hausdorff gap from p 63
3.4 A general theory of subadditive functions onwi 66
3.5 Conditional weakly null sequences based on
subadditive functions 77
4 Coherent Mappings and Trees
4.1 Coherent mappings 91
4.2 Lipschitz property of coherent trees 95
4.3 The global structure of the class of coherent trees 108
4.4 Lexicographically ordered coherent trees 124
4.5 Stationary C lines 128
5 The Square bracket Operation on Countable Ordinals
5.1 The upper trace and the square bracket operation 133
5.2 Projecting the square bracket operation 139
5.3 Some geometrical applications of the
square bracket operation 144
vi Contents
5.4 A square bracket operation from a special Aronszajn tree 152
5.5 A square bracket operation from the complete binary tree 157
6 General Walks and Their Characteristics
6.1 The full code and its application in
characterizing Mahlo cardinals 161
6.2 The weight function and its local versions 174
6.3 Unboundedness of the number of steps 178
7 Square Sequences
7.1 Square sequences and their full lower traces 187
7.2 Square sequences and local versions of p 195
7.3 Special square sequence and the corresponding function p 202
7.4 The function p on successors of regular cardinals 205
7.5 Forcing constructions based on p 213
7.6 The function p on successors of singular cardinals 220
8 The Oscillation Mapping and the Square bracket Operation
8.1 The oscillation mapping 233
8.2 The trace filter and the square bracket operation 243
8.3 Projections of the square bracket operation
on accessible cardinals 251
8.4 Two more variations on the square bracket operation 257
9 Unbounded Functions
9.1 Partial square sequences 271
9.2 Unbounded subadditive functions 273
9.3 Chang s conjecture and 02 277
9.4 Higher dimensions and the continuum hypothesis 283
10 Higher Dimensions
10.1 Stepping up to higher dimensions 289
10.2 Chang s conjecture as a 3 dimensional
Ramsey theoretic statement 294
10.3 Three dimensional oscillation mapping 298
10.4 Two cardinal walks 305
Bibliography 313
Index 321
|
| adam_txt |
Contents
1 Introduction
1.1 Walks and the metric theory of ordinals 1
1.2 Summary of results 10
1.3 Prerequisites and notation 17
1.4 Acknowledgements 18
2 Walks on Countable Ordinals
2.1 Walks on countable ordinals and their basic characteristics 19
2.2 The coherence of maximal weights 29
2.3 Oscillations of traces 40
2.4 The number of steps and the last step functions 47
3 Metric Theory of Countable Ordinals
3.1 Triangle inequalities 55
3.2 Constructing a Souslin tree using p 58
3.3 A Hausdorff gap from p 63
3.4 A general theory of subadditive functions onwi 66
3.5 Conditional weakly null sequences based on
subadditive functions 77
4 Coherent Mappings and Trees
4.1 Coherent mappings 91
4.2 Lipschitz property of coherent trees 95
4.3 The global structure of the class of coherent trees 108
4.4 Lexicographically ordered coherent trees 124
4.5 Stationary C lines 128
5 The Square bracket Operation on Countable Ordinals
5.1 The upper trace and the square bracket operation 133
5.2 Projecting the square bracket operation 139
5.3 Some geometrical applications of the
square bracket operation 144
vi Contents
5.4 A square bracket operation from a special Aronszajn tree 152
5.5 A square bracket operation from the complete binary tree 157
6 General Walks and Their Characteristics
6.1 The full code and its application in
characterizing Mahlo cardinals 161
6.2 The weight function and its local versions 174
6.3 Unboundedness of the number of steps 178
7 Square Sequences
7.1 Square sequences and their full lower traces 187
7.2 Square sequences and local versions of p 195
7.3 Special square sequence and the corresponding function p 202
7.4 The function p on successors of regular cardinals 205
7.5 Forcing constructions based on p 213
7.6 The function p on successors of singular cardinals 220
8 The Oscillation Mapping and the Square bracket Operation
8.1 The oscillation mapping 233
8.2 The trace filter and the square bracket operation 243
8.3 Projections of the square bracket operation
on accessible cardinals 251
8.4 Two more variations on the square bracket operation 257
9 Unbounded Functions
9.1 Partial square sequences 271
9.2 Unbounded subadditive functions 273
9.3 Chang's conjecture and 02 277
9.4 Higher dimensions and the continuum hypothesis 283
10 Higher Dimensions
10.1 Stepping up to higher dimensions 289
10.2 Chang's conjecture as a 3 dimensional
Ramsey theoretic statement 294
10.3 Three dimensional oscillation mapping 298
10.4 Two cardinal walks 305
Bibliography 313
Index 321 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 513 - Arithmetic |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:04:28Z |
| indexdate | 2024-07-09T20:59:29Z |
| institution | BVB |
| isbn | 9783764385286 3764385286 |
| language | English |
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| physical | VI, 324 Seiten Diagramme |
| publishDate | 2007 |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Todorcevic, Stevo 1965- Verfasser (DE-588)115235620 aut Walks on ordinals and their characteristics Stevo Todorcevic Basel [u.a.] Birkhäuser 2007 VI, 324 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Progress in mathematics Volume 263 Nombres ordinaux Nombres, Théorie des Number theory Numbers, Ordinal Rekursion (DE-588)4191814-9 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Rekursion (DE-588)4191814-9 s DE-604 Progress in mathematics Volume 263 (DE-604)BV000004120 263 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015731224&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Todorcevic, Stevo 1965- Walks on ordinals and their characteristics Progress in mathematics Nombres ordinaux Nombres, Théorie des Number theory Numbers, Ordinal Rekursion (DE-588)4191814-9 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4191814-9 (DE-588)4067277-3 |
| title | Walks on ordinals and their characteristics |
| title_auth | Walks on ordinals and their characteristics |
| title_exact_search | Walks on ordinals and their characteristics |
| title_exact_search_txtP | Walks on ordinals and their characteristics |
| title_full | Walks on ordinals and their characteristics Stevo Todorcevic |
| title_fullStr | Walks on ordinals and their characteristics Stevo Todorcevic |
| title_full_unstemmed | Walks on ordinals and their characteristics Stevo Todorcevic |
| title_short | Walks on ordinals and their characteristics |
| title_sort | walks on ordinals and their characteristics |
| topic | Nombres ordinaux Nombres, Théorie des Number theory Numbers, Ordinal Rekursion (DE-588)4191814-9 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Nombres ordinaux Nombres, Théorie des Number theory Numbers, Ordinal Rekursion Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015731224&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT todorcevicstevo walksonordinalsandtheircharacteristics |