Finite model theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Ausgabe: | 2., rev. and enl. ed. |
| Schriftenreihe: | Perspectives in mathematical logic
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 339 - 347 |
| Beschreibung: | XIII, 360 S. graph. Darst. |
| ISBN: | 3540657584 |
Internformat
MARC
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| 245 | 1 | 0 | |a Finite model theory |c Heinz-Dieter Ebbinghaus ; Jörg Flum |
| 250 | |a 2., rev. and enl. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIII, 360 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Perspectives in mathematical logic | |
| 500 | |a Literaturverz. S. 339 - 347 | ||
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| 650 | 0 | 7 | |a Modelltheorie |0 (DE-588)4114617-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127379179700224 |
|---|---|
| adam_text | Table of Contents
Preface VII
1. Preliminaries 1
2. The Ehrenfeucht Fraisse Method 13
2.1 Elementary Classes 13
2.2 Ehrenfeucht s Theorem 15
2.3 Examples and Fra isso s Theorem 20
2.4 Hanf s Theorem 26
2.5 Gaifman s Theorem 30
3. More on Games 37
3.1 Second Order Logic 37
3.2 Infinitary Logic: The Logics LXu,. and L^., ^ 40
3.3 The Logics FOS and L^ 40
3.3.1 Pebble Games 49
3.3.2 The s Invariant of a Structure 54
3.3.3 Scott Formulas 56
3.4 Logics with Counting Quantifiers 58
3.5 Failure of Classical Theorems in the Finite 62
4. 0—1 Laws 71
4.1 0 1 Laws for FO and L*^, 71
4.2 Parametric Classes 74
4.3 Unlabeled 0 1 Laws 77
4.3.1 Appendix 82
4.4 Examples and Consequences 84
4.5 Probabilities of Monadic Second Order Properties 88
5. Satisfiability in the Finite 95
5.1 Finite Model Property of FO2 95
5.2 Finite Model Property of V23* 5entences 99
XII Table of Contents
6. Finite Automata and Logic: A Microcosm of Finite Model
Theory 105
6.1 Languages Accepted by Automata 105
6.2 Word Models 108
6.3 Examples and Applications Ill
6.4 First Order Definability 114
7. Descriptive Complexity Theory 119
7.1 Some Extensions of First Order Logic 120
7.2 Turing Machines and Complexity Classes 124
7.2.1 Digression: Trahtenbrot s Theorem 127
7.2.2 Structures as Inputs 129
7.3 Logical Descriptions of Computations 133
7.4 The Complexity of the Satisfaction Relation 147
7.5 The Main Theorem and Some Consequences 151
7.5.1 Appendix 162
8. Logics with Fixed Point Operators 165
8.1 Inflationary and Least Fixed Points 165
8.2 Simultaneous Induction and Transitivity 177
8.3 Partial Fixed Point Logic 191
8.4 Fixed Point Logics and L£,w 198
8.4.1 The Logic FO(PFPPTime) 205
8.4.2 Fixed Point Logic with Counting 207
8.5 Fixed Point Logics and Second Order Logic 210
8.5.1 Digression: Implicit Definability 217
8.6 Transitive Closure Logic 220
8.6.1 FO(DTC) FO(TC) 221
8.6.2 FO(posTC) and Normal Forms 224
8.6.3 FO(TC) FO(LFP) 229
8.7 Bounded Fixed Point Logic 235
9. Logic Programs 239
9.1 DATALOG 239
9.2 I DATALOG and P DATALOG 245
9.3 A Preservation Theorem 250
9.4 Normal Forms for Fixed Point Logics 253
9.5 An Application of Negative Fixed Point Logic 263
9.6 Hierarchies of Fixed Point Logics 268
10. Optimization Problems 275
10.1 Polynomially Bounded Optimization Problems 275
10.2 Approximable Optimization Problems 280
Table of Contents XIII
11. Logics for PTIME 287
11.1 Logics and Invariants 288
11.2 PTIME on Classes of Structures 295
12. Quantifiers and Logical Reductions 307
12.1 Lindstrom Quantifiers 308
12.2 PTIME and Quantifiers 314
12.3 Logical Reductions 320
12.4 Quantifiers and Oracles 330
References 339
Index 349
|
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| author | Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944- |
| author_GND | (DE-588)107046857 (DE-588)121343391 |
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| author_sort | Ebbinghaus, Heinz-Dieter 1939- |
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| building | Verbundindex |
| bvnumber | BV012715392 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.7 |
| callnumber-search | QA9.7 |
| callnumber-sort | QA 19.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 |
| classification_tum | MAT 032f |
| ctrlnum | (OCoLC)247592271 (DE-599)BVBBV012715392 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2., rev. and enl. ed. |
| format | Book |
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| id | DE-604.BV012715392 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:24Z |
| institution | BVB |
| isbn | 3540657584 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008643972 |
| oclc_num | 247592271 |
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| owner_facet | DE-824 DE-20 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-739 DE-634 DE-83 DE-11 DE-188 |
| physical | XIII, 360 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Perspectives in mathematical logic |
| spelling | Ebbinghaus, Heinz-Dieter 1939- Verfasser (DE-588)107046857 aut Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum 2., rev. and enl. ed. Berlin [u.a.] Springer 1999 XIII, 360 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematical logic Literaturverz. S. 339 - 347 Modelltheorie Modelltheorie (DE-588)4114617-7 gnd rswk-swf Endliche Modelltheorie (DE-588)4615978-2 gnd rswk-swf Modelltheorie (DE-588)4114617-7 s DE-604 Endliche Modelltheorie (DE-588)4615978-2 s Flum, Jörg 1944- Verfasser (DE-588)121343391 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008643972&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944- Finite model theory Modelltheorie Modelltheorie (DE-588)4114617-7 gnd Endliche Modelltheorie (DE-588)4615978-2 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4615978-2 |
| title | Finite model theory |
| title_auth | Finite model theory |
| title_exact_search | Finite model theory |
| title_full | Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum |
| title_fullStr | Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum |
| title_full_unstemmed | Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum |
| title_short | Finite model theory |
| title_sort | finite model theory |
| topic | Modelltheorie Modelltheorie (DE-588)4114617-7 gnd Endliche Modelltheorie (DE-588)4615978-2 gnd |
| topic_facet | Modelltheorie Endliche Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008643972&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ebbinghausheinzdieter finitemodeltheory AT flumjorg finitemodeltheory |