A shorter model theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | 1. publ., digital print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 310 S. |
| ISBN: | 0521587131 |
Internformat
MARC
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| 100 | 1 | |a Hodges, Wilfrid |d 1941- |e Verfasser |0 (DE-588)108085392 |4 aut | |
| 245 | 1 | 0 | |a A shorter model theory |c Wilfrid Hodges |
| 250 | |a 1. publ., digital print. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a X, 310 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Model theory | |
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Datensatz im Suchindex
| _version_ | 1804137206700310528 |
|---|---|
| adam_text | CONTENTS
Introduction
vii
Note
on notation
ix
1
Naming of parts
1
1.1
Structures
2
1.2
Homomorphisms and substructures
5
1.3
Terms and atomic formulas
10
1.4
Parameters and diagrams
15
1.5
Canonical models
17
Further reading
20
2
Classifying structures
21
2.1
Definable subsets
22
2.2
Definable classes of structures
30
2.3
Some notions from logic
37
2.4
Maps and the formulas they preserve
43
2.5
Classifying maps by formulas
48
2.6
Translations
51
2.7
Quantifier elimination
59
Further reading
68
3
Structures that look alike
69
3.1
Theorems of Skolem
69
3.2
Back-and-forth equivalence
73
3.3
Games for elementary equivalence
82
Further reading
91
4
Interpretations
93
4.1
Automorphisms
94
4.2
Relativisation
101
4.3
Interpreting one structure in another
107
4.4
Imaginary elements
113
Further reading
122
5
The first-order case: compactness
124
5.1
Compactness for first-order logic
124
5.2
Types
130
5.3
Elementary amalgamation
134
5.4
Amalgamation and preservation
141
5.5
Expanding the language
147
5.6
Indiscernibles
152
Further reading
156
158
158
165
171
175
181
182
183
188
195
201
208
210
211
220
225
233
237
248
250
251
257
264
273
286
296
298
Index
300
б
The countable case
6.1
Fraïssé s
construction
6.2
Omitting types
6.3
Countable categoricity
6.4
co-categorical structures by
Fraïssé s
method
Further reading
7
The existential case
7.1
Existentially closed structures
7.2
Constructing e.c. structures
7.3
Model-completeness
7.4
Quantifier elimination revisited
Further reading
8
Saturation
8.1
The great and the good
8.2
Big models exist
8.3
Syntactic characterisations
8.4
One-cardinal and two-cardinal theorems
8.5
Ultraproducts and ultrapowers
Further reading
9
Structure and categoricity
9.1
Ehrenfeucht-Mostowski models
9.2
Minimal sets
9.3
Totally transcendental structures
9.4
Stability
9.5
Morley s theorem
Further reading
Index to symbols
|
| adam_txt |
CONTENTS
Introduction
vii
Note
on notation
ix
1
Naming of parts
1
1.1
Structures
2
1.2
Homomorphisms and substructures
5
1.3
Terms and atomic formulas
10
1.4
Parameters and diagrams
15
1.5
Canonical models
17
Further reading
20
2
Classifying structures
21
2.1
Definable subsets
22
2.2
Definable classes of structures
30
2.3
Some notions from logic
37
2.4
Maps and the formulas they preserve
43
2.5
Classifying maps by formulas
48
2.6
Translations
51
2.7
Quantifier elimination
59
Further reading
68
3
Structures that look alike
69
3.1
Theorems of Skolem
69
3.2
Back-and-forth equivalence
73
3.3
Games for elementary equivalence
82
Further reading
91
4
Interpretations
93
4.1
Automorphisms
94
4.2
Relativisation
101
4.3
Interpreting one structure in another
107
4.4
Imaginary elements
113
Further reading
122
5
The first-order case: compactness
124
5.1
Compactness for first-order logic
124
5.2
Types
130
5.3
Elementary amalgamation
134
5.4
Amalgamation and preservation
141
5.5
Expanding the language
147
5.6
Indiscernibles
152
Further reading
156
158
158
165
171
175
181
182
183
188
195
201
208
210
211
220
225
233
237
248
250
251
257
264
273
286
296
298
Index
300
б
The countable case
6.1
Fraïssé's
construction
6.2
Omitting types
6.3
Countable categoricity
6.4
co-categorical structures by
Fraïssé's
method
Further reading
7
The existential case
7.1
Existentially closed structures
7.2
Constructing e.c. structures
7.3
Model-completeness
7.4
Quantifier elimination revisited
Further reading
8
Saturation
8.1
The great and the good
8.2
Big models exist
8.3
Syntactic characterisations
8.4
One-cardinal and two-cardinal theorems
8.5
Ultraproducts and ultrapowers
Further reading
9
Structure and categoricity
9.1
Ehrenfeucht-Mostowski models
9.2
Minimal sets
9.3
Totally transcendental structures
9.4
Stability
9.5
Morley's theorem
Further reading
Index to symbols |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hodges, Wilfrid 1941- |
| author_GND | (DE-588)108085392 |
| author_facet | Hodges, Wilfrid 1941- |
| author_role | aut |
| author_sort | Hodges, Wilfrid 1941- |
| author_variant | w h wh |
| building | Verbundindex |
| bvnumber | BV022960225 |
| classification_rvk | CC 2600 SK 130 |
| ctrlnum | (OCoLC)474010668 (DE-599)BVBBV022960225 |
| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
| edition | 1. publ., digital print. |
| format | Book |
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| id | DE-604.BV022960225 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:04:28Z |
| indexdate | 2024-07-09T21:08:37Z |
| institution | BVB |
| isbn | 0521587131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016164605 |
| oclc_num | 474010668 |
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| owner_facet | DE-739 DE-19 DE-BY-UBM |
| physical | X, 310 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Hodges, Wilfrid 1941- Verfasser (DE-588)108085392 aut A shorter model theory Wilfrid Hodges 1. publ., digital print. Cambridge [u.a.] Cambridge Univ. Press 2003 X, 310 S. txt rdacontent n rdamedia nc rdacarrier Model theory Modelltheorie (DE-588)4114617-7 gnd rswk-swf Modelltheorie (DE-588)4114617-7 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016164605&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hodges, Wilfrid 1941- A shorter model theory Model theory Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4114617-7 |
| title | A shorter model theory |
| title_auth | A shorter model theory |
| title_exact_search | A shorter model theory |
| title_exact_search_txtP | A shorter model theory |
| title_full | A shorter model theory Wilfrid Hodges |
| title_fullStr | A shorter model theory Wilfrid Hodges |
| title_full_unstemmed | A shorter model theory Wilfrid Hodges |
| title_short | A shorter model theory |
| title_sort | a shorter model theory |
| topic | Model theory Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Model theory Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016164605&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hodgeswilfrid ashortermodeltheory |