A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fundamenta Mathematicae, ## (####), pp. ###--###. Home/Search Document Not in Database Summary Related Articles Check |
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Definable Relations and First-Order Query Languages.. - Benedikt, Libkin.. (Correct)
....each consistent type (a type is consistent if it has a witness in at least one model of Omega ) over a finite set A in FO(M) is satisfied in M . It is known [21] that every model M over Omega has an elementary equivalent saturated model M . 6 Many proofs use Ehrenfeucht Frasse games [28, 33, 27]. For two structures M 1 and M 2 of the same vocabulary, we write M 1 j k M 2 if the duplicator has a winning strategy in the k round game on M 1 and M 2 (that is, if M 1 and M 2 agree on all sentences of quantifier rank up to k) We also assume familiarity with Monadic Second Order Logic (MSO) ....
A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fund. Math., 49:129--141, 1961.
Logic and Random Structures - Spencer (Correct)
....have the same truth value as R(y i 1 , y i l ) for every choice of i 1 , i l from 1, t. About the references Among the other surveys of this area we recommend those of Compton [3] Winkler [26] Lynch [15] and this author [23] The Ehrenfeucht game was first given in [5]. It was essentially found in earlier work by Fraisse and is sometimes referred to as the Ehrenfeucht Fraisse game. The classic Zero One law for random graphs with p = often called the uniform distribution) are due to Glebskii et al. 8] and Fagin [7] The classic paper that began the ....
A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fundam. Math. 49 (1961), 129-141
Definable Relations and First-Order Query Languages.. - Benedikt, Libkin.. (Correct)
....M is a model such that each consistent type (a type is consistent if it has a witness in at least one model of over a nite set A in FO(M) is satis ed in M . It is known [21] that every model M has an elementary equivalent saturated model M . Many proofs use Ehrenfeucht Fra ss e games [28, 33, 27]. For two structures M 1 and M 2 of the same vocabulary, we write M 1 k M 2 if the duplicator has a winning strategy in the k round game on M 1 and M 2 (that is, if M 1 and M 2 agree on all sentences of quanti er rank up to k) We also assume familiarity with Monadic Second Order Logic (MSO) ....
A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fund. Math., 49:129-141, 1961.
Structure and Complexity of Relational Queries - Chandra, Harel (1982) (193 citations) (Correct)
....The domain elements correspond to game positions, Move 108 CHANDRAAND HAREL corresponds to the next move relation, and Win determines if the position is a win for the first player. Now by Lemma 3.5, the corresponding query QA is in 0 2. We show by the technique of Ehrenfeucht Frai ss6 games [10, 13] that QA o by showing that if the expression C = Start, Move, Win. 3j71) j72) represents a query Qc in 2 o, then there are data bases B, B such that QB) Q,B ) but Qc(B) Qc(B ) Note that ( D O and =D DD . Let k be the maximum number of variables in any We first ....
....Biff Win (d) holds holds in likewise for Start, and for every p, q, Move(dp, dq) holds in Biff Move (d, d)holds B 0 = B 6 = 0 FIG. 1. win for first player; not a win for first player. in B . Otherwise, the first player wins. From (a minor modification of) the Ehrenfeucht Fra iss6 theorem [10, 13], it follows that if the second player has a winning strategy, then Qc(B) Qc(B ) We shall show that the second player indeed has a winning strategy. In fact, we shall show that the second player wins even an i I move game, where the first player must start choosing elements from B = B , The ....
A. EHRENFEUCHT, An application of games to the completeness problem for formalized theores, Fund. Math 49 (1961), 129-141.
Completeness Results for Recursive Data Bases - Hirst, Harel (1996) (11 citations) (Correct)
....satisfy precisely the same 528 first order formulas with up to r quantifiers and n free variables. An additional well known characterization is that u r V iiT the duplicator has a winning strategy in the r round first order Ehrenfeucht Fraisse Game (r game, for short) played on (B, u) and (B, v) [E, Fr]. It is easy to see that it suffices to have the quantifiers range over nodes in T o, since To contains representatives of all the equivalence classes: PROPOSITION 3.4. Let u, v D and u , v r n, such that u o u and v o v . Then, for all r, U r 1 V iff VaT(u )3bT(v )u a=rv b and Vb T(v ) ....
A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fund. Math. 49 (1961), 129- 141.
An Ehrenfeucht-Fraïssé Game Approach to Collapse.. - Schweikard Self-citation (Ehrenfeucht) (Correct)
....results in database theory. We show that, in principle, all collapse results of the kind fixed in Definition 3.9 can be proved via Ehrenfeucht Fra iss6 games. 4. 1 The Ehrenfeucht Fra iss6 Game for FO Ehrenfeucht Fra iss6 games, for short: EF games, were invented by Ehrenfeucht and Fra iss6 in [12, 14]. These combinatorial games are particularly useful for investigating what can, and what cannot, be expressed in various logics. A well written survey on EF games is, e.g. given by Fagin in [13] More details can be found in the textbooks [18, 11] In the present section we will concentrate on ....
A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fun- damenta Mathematicae, 49:129 141, 1961.
MSO Zero One Laws on Random Labelled Acyclic Graphs - McColm Self-citation (Ehrenfeucht) (Correct)
....Similarly, if there are but finitely many (k; l) EF equivalence classes, and hence finitely many (k; l) EF types, there are finitely many (k 1; l) EF types, and hence finitely (k 1; l) EF equivalence classes. Xi 6 The following was actually proven directly in [9] the first order case is in [8]) see [6] Corollary 2.1 For each k, l, there are finitely many (k; l) types for each schema. In addition, for each MSO sentence and each pair of structures A and B, all of a common schema, if is of joint depth (k; l) and if A j k;l B, then A j= iff B j= We will often say that if A is ....
A. Ehrenfeucht, An Application of Games to the Completeness Problem for Formalized Theories, Fund. Math. 49 (1961), 129--141. 19
Unknown - Von Der Fakultt (Correct)
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A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fundamenta Mathematicae, ## (####), pp. ###--###.
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A. Ehrenfeucht, "An Application of Games to the Completeness Problem for Formalized Theories", Fund. Math. 49 (1961), 129-141.
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A. Ehrenfeucht. An application of games to the completeness problem of formalized theories. Fundamenta Mathematicae, 49 (1961), 129--141.
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A. Ehrenfeucht, An application of games to the completeness problem for formalizedtheories,Fundamentae Mathematicae 49 (1961), 129--141. 14
Decidability and Definability Results Related to the Elementary.. - Bes (Correct)
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A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49, 129--141, 1961.
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A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49:129--141, 1961.
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A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fund. Math., 49:129-141, 1961.
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A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49:129-141, 1961.
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