A course in model theory:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2012
|
| Ausgabe: | 1st publ. |
| Schriftenreihe: | Lecture notes in logic
40 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024970856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 248 S. graph. Darst. 23 cm |
| ISBN: | 052176324X 9780521763240 |
Internformat
MARC
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| 245 | 1 | 0 | |a A course in model theory |c Katrin Tent ; Martin Ziegler |
| 250 | |a 1st publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 2012 | |
| 300 | |a X, 248 S. |b graph. Darst. |c 23 cm | ||
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Datensatz im Suchindex
| _version_ | 1819331047595180032 |
|---|---|
| adam_text | CONTENTS
Preface
.............................................................. xi
Chapter
1.
The basics
.............................................. 1
1.1.
Structures
................................................. 1
1.2.
Language
................................................. 5
1.3.
Theories
.................................................. 13
Chapter
2.
Elementary extensions and compactness
............... 17
2.1.
Elementary substructures
.................................. 17
2.2.
The Compactness Theorem
................................ 19
2.3.
The
Löwenheim-Skolem
Theorem
......................... 24
Chapter
3.
Quantifier elimination
................................. 27
3.1.
Preservation theorems
..................................... 27
3.2.
Quantifier elimination
..................................... 31
3.3.
Examples
................................................. 37
Chapter
4.
Countable models
..................................... 47
4.1.
The omitting types theorem
................................ 47
4.2.
The space of types
......................................... 48
4.3.
Uo-categorical theories
..................................... 51
4.4.
The amalgamation method
................................ 55
4.5.
Prime models
............................................. 58
Chapter
5.
Hi-categorical theories
................................ 63
5.1.
Indiscernibles
............................................. 63
5.2.
ω
-stable theories
.......................................... 67
5.3.
Prime extensions
.......................................... 70
5.4.
Lachlan s Theorem
........................................ 73
5.5.
Vaughtian pairs
........................................... 75
5.6.
Algebraic formulas
........................................ 79
5.7.
Strongly minimal sets
...................................... 81
5.8.
The Baldwin-Lachlan Theorem
............................ 86
Chapter
6.
Morley rank
.......................................... 89
6.1.
Saturated models and the monster
.......................... 89
6.2.
Morley rank
.............................................. 95
6.3.
Countable models of Hi-categorical theories
................100
6.4.
Computation of Morley rank
..............................103
Chapter
7.
Simple theories
.........................................109
7.1.
Dividing and forking
......................................109
7.2.
Simplicity
.................................................112
7.3.
The independence theorem
................................ 118
7.4.
Lascar strong types
........................................123
7.5.
Example: pseudo-finite fields
.............................. 126
Chapter
8.
Stable theories
........................................ 129
8.1.
Heirs and coheirs
..........................................129
8.2.
Stability
..................
-<¿,
.............................. 132
8.3.
Definable types
........
:
. :................................135
8.4.
Elimination of
imaginarles
and
Teą
........................ 139
8.5.
Properties of forking in stable theories
......................145
8.6.
SU-rank and the stability spectrum
.........................151
Chapter
9.
Prime extensions
....................................... 157
9.1.
Indiscernibles
in stable theories
............................ 157
9.2.
Totally transcendental theories
.............................159
9.3.
Countable stable theories
..................................162
Chapter
10.
The fine structure of
К
і
-categorical theories
........165
10.1.
Internal types
.............................................165
10.2.
Analysable
types
.......................................... 168
10.3.
Locally modular strongly minimal sets
..................... 172
10.4.
Hrushovski s examples
.....................................175
Appendix A. Set theory
............................................185
A.I. Sets and classes
........................................... 185
A.2. Ordinals
..................................................186
A.3. Cardinals
.................................................188
Appendix B. Fields
.................................................191
B.I. Ordered fields
.............................................191
B.2. Differential fields
..........................................194
B.3. Separable and regular field extensions
......................198
B.4. Pseudo-finite fields and
profinite
groups
....................201
Appendix
С
Combinatorics
........................................205
C.I. Pregeometries
.............................................205
C.2.
The Erdős-Makkai
Theorem
..............................210
С.З.
The
Erdós-Rado
Theorem
.................................210
Appendix
D.
Solutions to exercises
................................213
References
..........................................................235
Index
................................................................239
|
| any_adam_object | 1 |
| author | Tent, Katrin 1963- Ziegler, Martin 1968- |
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| ctrlnum | (OCoLC)796212425 (DE-599)BSZ358375452 |
| dewey-full | 511.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.34 |
| dewey-search | 511.34 |
| dewey-sort | 3511.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st publ. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV040114618 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:08:23Z |
| institution | BVB |
| isbn | 052176324X 9780521763240 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024970856 |
| oclc_num | 796212425 |
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| owner_facet | DE-11 DE-20 DE-188 DE-739 DE-19 DE-BY-UBM |
| physical | X, 248 S. graph. Darst. 23 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Lecture notes in logic |
| series2 | Lecture notes in logic |
| spellingShingle | Tent, Katrin 1963- Ziegler, Martin 1968- A course in model theory Lecture notes in logic Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4123623-3 |
| title | A course in model theory |
| title_auth | A course in model theory |
| title_exact_search | A course in model theory |
| title_full | A course in model theory Katrin Tent ; Martin Ziegler |
| title_fullStr | A course in model theory Katrin Tent ; Martin Ziegler |
| title_full_unstemmed | A course in model theory Katrin Tent ; Martin Ziegler |
| title_short | A course in model theory |
| title_sort | a course in model theory |
| topic | Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Modelltheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024970856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008909514 |
| work_keys_str_mv | AT tentkatrin acourseinmodeltheory AT zieglermartin acourseinmodeltheory |