Models and games:
This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tablea...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
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| Schriftenreihe: | Cambridge studies in advanced mathematics
132 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (ix, 367 Seiten) |
| ISBN: | 9780511974885 |
| DOI: | 10.1017/CBO9780511974885 |
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Datensatz im Suchindex
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| author | Väänänen, Jouko 1950- |
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| author_sort | Väänänen, Jouko 1950- |
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| bvnumber | BV043942086 |
| classification_rvk | CC 2400 SK 130 |
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| contents | Introduction -- Preliminaries and notation -- Games -- Graphs -- Models -- First-order logic -- Infinitary logic -- Model theory of infinitary logic -- Stronger infinitary logics -- Generalized quantifiers |
| ctrlnum | (ZDB-20-CBO)CR9780511974885 (OCoLC)839017976 (DE-599)BVBBV043942086 |
| 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 Philosophie |
| doi_str_mv | 10.1017/CBO9780511974885 |
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| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511974885 |
| language | English |
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| spelling | Väänänen, Jouko 1950- Verfasser (DE-588)121630544 aut Models and games Jouko Väänänen Models & Games Cambridge Cambridge University Press 2011 1 Online-Ressource (ix, 367 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 132 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- Preliminaries and notation -- Games -- Graphs -- Models -- First-order logic -- Infinitary logic -- Model theory of infinitary logic -- Stronger infinitary logics -- Generalized quantifiers This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications Model theory Modelltheorie (DE-588)4114617-7 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Logik (DE-588)4036202-4 s DE-604 Modelltheorie (DE-588)4114617-7 s Erscheint auch als Druck-Ausgabe 978-0-521-51812-3 Cambridge studies in advanced mathematics 132 (DE-604)BV044781283 132 https://doi.org/10.1017/CBO9780511974885 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Väänänen, Jouko 1950- Models and games Cambridge studies in advanced mathematics Introduction -- Preliminaries and notation -- Games -- Graphs -- Models -- First-order logic -- Infinitary logic -- Model theory of infinitary logic -- Stronger infinitary logics -- Generalized quantifiers Model theory Modelltheorie (DE-588)4114617-7 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4036202-4 (DE-588)4151278-9 |
| title | Models and games |
| title_alt | Models & Games |
| title_auth | Models and games |
| title_exact_search | Models and games |
| title_full | Models and games Jouko Väänänen |
| title_fullStr | Models and games Jouko Väänänen |
| title_full_unstemmed | Models and games Jouko Väänänen |
| title_short | Models and games |
| title_sort | models and games |
| topic | Model theory Modelltheorie (DE-588)4114617-7 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Model theory Modelltheorie Logik Einführung |
| url | https://doi.org/10.1017/CBO9780511974885 |
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