Models and games:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Cambridge [u.a.]
Cambridge University Press
2011
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
132 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 367 S. Ill., graph. Darst. 23 cm |
| ISBN: | 9780521518123 0521518121 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804145791063818240 |
|---|---|
| adam_text | Contents
Preface
page
*>
1
Introduction
1
2
Preliminaries and Notation
3
2.1
Finite Sequences
3
2.2
Equipollence
5
2.3
Countable sets
6
2.4
Ordinals
7
2.5
Cardinals
9
2.6
Axiom of Choice
10
2.7
Historical Remarks and References
11
Exercises
1 1
3
Games
14
3.1
Introduction
14
3.2
Two-Person Games of Perfect Information
14
3.3
The Mathematical Concept of Game
20
3.4
Game Positions
21
3.5
Infinite Games
24
3.6
Historical Remarks and References
28
Exercises
28
4
Graphs
35
4.1
Introduction
35
4.2
First-Order Language of Graphs
35
4.3
The
Ehren
feucht-Fraïssé
Game on Graphs
38
4.4
Ehrenfeucht-Fraïssé
Games and Elementary Equivalence
43
4.5
Historical Remarks and References
48
Exercises
49
viii
Contents
5 Models 53
5.1
Introduction
53
5.2 Basic
Concepts
54
5.3
Substructures
62
5.4
Back-and-Forth Sets
63
5.5
The
Ehrenfeucht-Fraïssé
Game
65
5.6
Back-and-Forth Sequences
69
5.7
Historical Remarks and References
71
Exercises
71
6
First-Order Logic
79
6.1
Introduction
79
6.2
Basic Concepts
79
6.3
Characterizing Elementary Equivalence
81
6.4
The
Löwenheim-Skolem
Theorem
85
6.5
The Semantic Game
93
6.6
The Model Existence Game
98
6.7
Applications
102
6.8
Interpolation
107
6.9
Uncountable Vocabularies
113
6.10
Ultraproducts
119
6.11
Historical Remarks and References
125
Exercises
126
7
Infìnitary
Logic
139
7.1
Introduction
139
7.2
Preliminary Examples
139
7.3
The Dynamic
Ehrenfeucht-Fraïssé
Game
144
7.4
Syntax and Semantics of Infinitary Logic
157
7.5
Historical Remarks and References
170
Exercises
171
8
Model Theory of Infinitary Logic
176
8.1
Introduction
176
8.2 Löwenheim—
Skolem Theorem for Loo^
176
8.3
Model Theory of
LWlU,
179
8.4
Large Models
184
8.5
Model Theory of LK+UJ
191
8.6
Game Logic
201
8.7
Historical Remarks and References
222
Exercises
223
Contents ix
9
Stronger Infinitary Logics
228
9.1
Introduction
228
9.2
Infinite Quantifier Logic
228
9.3
The
Transfinite
Ehrenfeucht-Fraïssé
Game
249
9.4
A Quasi-Order of Partially Ordered Sets
254
9.5
The
Transfinite
Dynamic
Ehrenfeucht-Fraïssé
Game
258
9.6
Topology of Uncountable Models
270
9.7
Historical Remarks and References
275
Exercises
278
10
Generalized Quantifiers
283
10.1
Introduction
283
10.2
Generalized Quantifiers
284
10.3
The
Ehrenfeucht-Fraïssé
Game of
Q
296
10.4
First-Order Logic with a Generalized Quantifier
307
10.5
Ułtraproducts
and Generalized Quantifiers
312
1
0.6
Axioms for Generalized Quantifiers
314
10.7
The Cofinality Quantifier
333
10.8
Historical Remarks and References
342
Exercises
343
References
353
index
362
|
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| discipline | Mathematik Philosophie |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:25:03Z |
| institution | BVB |
| isbn | 9780521518123 0521518121 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022632101 |
| oclc_num | 729995541 |
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| owner | DE-19 DE-BY-UBM DE-20 DE-703 |
| owner_facet | DE-19 DE-BY-UBM DE-20 DE-703 |
| physical | IX, 367 S. Ill., graph. Darst. 23 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Väänänen, Jouko 1950- Verfasser (DE-588)121630544 aut Models and games Jouko Vaananen 1. publ. Cambridge [u.a.] Cambridge University Press 2011 IX, 367 S. Ill., graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 132 Logik (DE-588)4036202-4 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Model theory (DE-588)4151278-9 Einführung gnd-content Logik (DE-588)4036202-4 s DE-604 Modelltheorie (DE-588)4114617-7 s Cambridge studies in advanced mathematics 132 (DE-604)BV000003678 132 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022632101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Väänänen, Jouko 1950- Models and games Cambridge studies in advanced mathematics Logik (DE-588)4036202-4 gnd Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4114617-7 (DE-588)4151278-9 |
| title | Models and games |
| title_auth | Models and games |
| title_exact_search | Models and games |
| title_full | Models and games Jouko Vaananen |
| title_fullStr | Models and games Jouko Vaananen |
| title_full_unstemmed | Models and games Jouko Vaananen |
| title_short | Models and games |
| title_sort | models and games |
| topic | Logik (DE-588)4036202-4 gnd Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Logik Modelltheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022632101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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