Models and GamesCambridge University Press, 05.05.2011 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. |
Inhalt
| 7 | |
5 | 29 |
1 | 35 |
3 | 41 |
Exercises | 49 |
Models | 53 |
Substructures | 62 |
6 | 69 |
Infinitary Logic | 139 |
Model Theory of Infinitary Logic | 176 |
Stronger Infinitary Logics | 228 |
Generalized Quantifiers | 283 |
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Häufige Begriffe und Wortgruppen
A₁ assume atomic automorphisms Axiom of Choice b₁ back-and-forth sequence back-and-forth set bijection cardinality cofinality Compactness Theorem consistent constant symbols countable models countable vocabulary Craig Interpolation defined Definition denote Ehrenfeucht-Fraïssé Game element equivalence relation Example Exercise Figure first-order logic following are equivalent G and G game G Gcub Geub induction hypothesis infinitary logic infinite L-formula L-sentences L-structure Lemma linear order Loow Löwenheim-Skolem Theorem MEG(T model theory monotone moves natural number ordinal partial isomorphism player I plays player II player II chooses player II wins po-set Proof Let Proof Suppose Proposition prove quantifier Q quantifier rank satisfies sentence of quantifier SG(M Show that player Skolem function strategy in EFD strategy of player structure subset Suppose G ultraproduct uncountable Väänänen Vaught vertex vertices w₁ well-order winning strategy