The determinacy of long games
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
<<de>> Gruyter
2004
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| Schriftenreihe: | De Gruyter series in logic and its applications
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Neeman, Itay |d 1972- |e Verfasser |0 (DE-588)129592463 |4 aut | |
| 245 | 1 | 0 | |a The determinacy of long games |c Itay Neeman |
| 264 | 1 | |a Berlin [u.a.] |b <<de>> Gruyter |c 2004 | |
| 300 | |a XI, 317 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in logic and its applications |v 7 | |
| 500 | |a Literaturverz. S. 309 - 311 | ||
| 650 | 4 | |a Determinants | |
| 650 | 4 | |a Game theory | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 0 | 7 | |a Spieltheorie |0 (DE-588)4056243-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mengenlehre |0 (DE-588)4074715-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Spieltheorie |0 (DE-588)4056243-8 |D s |
| 689 | 0 | 1 | |a Mengenlehre |0 (DE-588)4074715-3 |D s |
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| 830 | 0 | |a De Gruyter series in logic and its applications |v 7 |w (DE-604)BV012743398 |9 7 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-013086493 | |
Datensatz im Suchindex
| _version_ | 1819601235041320960 |
|---|---|
| adam_text | Contents
Preface vii
Introduction 1
1 Basic components 15
1A The auxiliary games map........................ 16
1A(1) Types.............................. 16
1A(2) The rules of the game...................... 20
IB Generic runs............................... 23
1C Pivots.................................. 27
1C(1) The game Apiv[x] ....................... 28
1C(2) Constructing (rpiv[Q,x]..................... 30
1C(3) Properties of (Tpiv........................ 35
ID Mirror images.............................. 37
IE Sample application........................... 39
IF Mixed pivots .............................. 43
1F(1) The game............................ 43
1F(2) The strategy amix[e. *]..................... 48
1F(3) Properties of CTmix........................ 49
2 Games of fixed countable length 51
2A General games and iteration games................... 51
2B Limits.................................. 56
2B(1) The basic definitions...................... 57
2B(2) I wins.............................. 59
2B(3) II wins ............................. 65
2B(4) The third case.......................... 66
2B(5) Summary............................ 68
2C Successors................................ 68
2D Limits again............................... 73
2D(1) II wins ............................. 75
2D(2) I wins.............................. 79
2D(3) Determinacy.......................... 80
2E Universally Baire sets.......................... 82
3 Games of continuously coded length 87
3A Codes.................................. 87
3B First determinacy result, part I..................... 89
3B(1) Names ............................. 89
3B(2) The basic step.......................... 93
Contents
3B(3) Iwins.............................. 96
3B(4) Discussion........................... 104
3B(5) Internal ultrapowers vs. copying................ 106
3C First determinacy result, part II..................... 109
3C(1) II wins ............................. 109
3C(2) Determinacy.......................... 112
3D A slight improvement.......................... 119
3D(1) Z^ functions.......................... 120
3D(2) T,oi+a functions......................... 124
3E Variation................................. 124
3E(1) A sketch of the proof...................... 129
Pullbacks 135
4A Codes.................................. 135
4B Woodin s extender algebra....................... 141
AC Names, partí.............................. 155
4C(1) Removing obstructions..................... 155
4C(2) Relative successors....................... 157
4C(3) Relative limits and records................... 158
4D Names, part II.............................. 162
4D(1) Woodin limits of Woodin cardinals............... 162
4D(2) Relative successors....................... 165
4D(3) Compositions.......................... 166
4D(4) Summary............................ 166
4E Mirror images.............................. 167
4E(1) Removing obstructions..................... 167
4E(2) Mirrored successor game.................... 168
4E(3) Relative limits and records................... 169
4E(4) Woodin limits of Woodin cardinals............... 172
4E(5) Relative successors....................... 173
4E(6) Compositions.......................... 174
4E(7) Summary............................ 174
When both players lose 175
5A Saturation................................ 175
5B Successors, basic step.......................... 181
5C Relative limits.............................. 183
5C(1) Basic step............................ 183
5C(2) Construction.......................... 187
5D Woodin limits of Woodin cardinals................... 194
5D(1) Basic step............................ 194
5D(2) Impossibility.......................... 197
5D(3) Another impossibility...................... 199
5D(4) Construction.......................... 201
Contents xi
5E Relative successors........................... 204
5F Compositions.............................. 205
5G Conclusion............................... 207
6 Along a single branch 209
6A The game................................ 209
6A(1) How to leap........................... 215
6A(2) The skipping game....................... 218
6B Successors, basic step.......................... 220
6C Relative limits.............................. 221
6C(1) Finite.............................. 222
6C(2) Infinite............................. 225
6C(3) Construction.......................... 228
6D Woodin limits of Woodin cardinals................... 235
6D(1) Hopeful............................. 235
6D(2) Not hopeful........................... 240
6D(3) Combined............................ 242
6E Relative successors and compositions ................. 244
6F Skips .................................. 248
6F(1) Routes ............................. 249
6F(2) Extensions........................... 255
6F(3) Closing skips.......................... 258
6F(4) Discussion........................... 260
6F(5) Safe positions.......................... 262
6F(6) The strategy........................... 264
6G Conclusion ............................... 266
7 Games which reach local cardinals 268
7A Shifted payoff.............................. 268
7B Layout.................................. 270
7B(1) Extensions........................... 276
7C Basic step................................ 277
7C(1) Obstruction free ........................ 280
7C(2) I-acceptably obstructed..................... 281
7C(3) Summary............................ 284
7D Construction............................... 285
7E The main theorem............................ 289
7F Determinacy............................... 292
A Extenders, generic extensions, and iterability 301
Bibliography 309
Index 313
|
| any_adam_object | 1 |
| author | Neeman, Itay 1972- |
| author_GND | (DE-588)129592463 |
| author_facet | Neeman, Itay 1972- |
| author_role | aut |
| author_sort | Neeman, Itay 1972- |
| author_variant | i n in |
| building | Verbundindex |
| bvnumber | BV019760123 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA269 |
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| classification_rvk | SK 860 |
| ctrlnum | (OCoLC)56532575 (DE-599)BVBBV019760123 |
| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019760123 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T18:11:26Z |
| institution | BVB |
| isbn | 3110183412 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013086493 |
| oclc_num | 56532575 |
| open_access_boolean | |
| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XI, 317 S. graph. Darst. 25 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter series in logic and its applications |
| series2 | De Gruyter series in logic and its applications |
| spellingShingle | Neeman, Itay 1972- The determinacy of long games De Gruyter series in logic and its applications Determinants Game theory Logic, Symbolic and mathematical Spieltheorie (DE-588)4056243-8 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4074715-3 |
| title | The determinacy of long games |
| title_auth | The determinacy of long games |
| title_exact_search | The determinacy of long games |
| title_full | The determinacy of long games Itay Neeman |
| title_fullStr | The determinacy of long games Itay Neeman |
| title_full_unstemmed | The determinacy of long games Itay Neeman |
| title_short | The determinacy of long games |
| title_sort | the determinacy of long games |
| topic | Determinants Game theory Logic, Symbolic and mathematical Spieltheorie (DE-588)4056243-8 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Determinants Game theory Logic, Symbolic and mathematical Spieltheorie Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013086493&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012743398 |
| work_keys_str_mv | AT neemanitay thedeterminacyoflonggames |