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POSITIONAL STRATEGIES IN LONG EHRENFEUCHT–FRAÏSSÉ GAMES

S. SHELAH, J. VÄÄNÄNEN, B. VELIČKOVIĆ
2015 Journal of Symbolic Logic (JSL)  
We prove that it is relatively consistent with ZF + CH that there exist two models of cardinality $\aleph _2 $ such that the second player has a winning strategy in the EhrenfeuchtFraïssé-game of length  ...  One can translate Karttunen's concept in terms of the existence of a winning strategy in a certain Ehrenfeucht-Fraïssé game which we now describe.  ...  Persistent families of functions In this section we change the original problem and instead of considering the Ehrenfeucht-Fraïssé game on a pair of structures, we consider a certain game on a given family  ... 
doi:10.1017/jsl.2014.43 fatcat:rdggjapgfzbgfbw27yzhfz2vyi

Positional strategies in long Ehrenfeucht-Fraissé games [article]

Saharon Shelah, Jouko Väänänen, Boban Velickovic
2013 arXiv   pre-print
We prove that it is relatively consistent with ZF + CH that there exist two models of cardinality \aleph_2 such that the second player has a winning strategy in the Ehrenfeucht-Fra\"iss\'e-game of length  ...  One can translate Karttunen's concept in terms of the existence of a winning strategy in a certain Ehrenfeucht-Fraïssé game which we now describe.  ...  Persistent families of functions In this section we change the original problem and instead of considering the Ehrenfeucht-Fraïssé game on a pair of structures, we consider a certain game on a given family  ... 
arXiv:1308.0156v1 fatcat:iqxsarb4lfhrzfrxr7khkglgxm

An Ehrenfeucht-Fraïssé Game for L_ω_1ω [article]

Jouko Väänänen, Tong Wang
2012 arXiv   pre-print
There was no Ehrenfeucht-Fraisse game for L_ω_1ω in the literature. In this paper we develop an Ehrenfeucht-Fraisse Game for L_ω_1ω.  ...  Ehrenfeucht-Fraisse games are very useful in studying separation and equivalence results in logic. The standard finite Ehrenfeucht-Fraisse game characterizes equivalence in first order logic.  ...  The Standard Ehrenfeucht-Fraïssé Game Let us first recapitulate the standard Ehrenfeucht-Fraïssé game in infinitary logic. Definition 2. Let L be a relational vocabulary and A, B be L-structures.  ... 
arXiv:1212.0108v1 fatcat:6k5w6ctgejafhica7de76evnoe

Two-Variable Ehrenfeucht-Fraisse Games over Omega-Terms [article]

Manfred Kufleitner, Jan Philipp Wächter
2014 arXiv   pre-print
Huschenbett and the first author have shown how to use infinite Ehrenfeucht-Fraisse games on linear orders for showing that some given fragment satisfies an identity of omega-terms (STACS 2014).  ...  Fragments of first-order logic over words can often be characterized in terms of finite monoids, and identities of omega-terms are an effective mechanism for specifying classes of monoids.  ...  Ehrenfeucht-Fraïssé Games In this section we will have a closer look on Ehrenfeucht-Fraïssé games.  ... 
arXiv:1411.0593v1 fatcat:vdg4ou6cafcxlchc34wfpjzjxe

A Practical Approach to Courcelle's Theorem

Joachim Kneis, Alexander Langer
2009 Electronical Notes in Theoretical Computer Science  
The proof uses a new technique based on using Hintikka game properties in dynamic programming.  ...  In 1990, Courcelle showed that every problem definable in Monadic Second-Order Logic (MSO) can be solved in linear time on graphs with bounded treewidth.  ...  Then A ≡ q B if and only if the duplicator has a winning strategy for the Ehrenfeucht-Fraïssé-game on A and B with q rounds [16, 11] .  ... 
doi:10.1016/j.entcs.2009.08.028 fatcat:335kmrop5bg5lhtk4c5l3vod6e

Finite-Degree Predicates and Two-Variable First-Order Logic [article]

Charles Paperman
2015 arXiv   pre-print
I also thank Michaël Cadilhac, Amy Hadfield, and the anonymous reviewers for their contribution in improving a lot the final version of this paper.  ...  Ehrenfeucht-Fraïssé game One of the important tools for proving our main result is the Ehrenfeucht-Fraïssé game for two-variable logic.  ...  In this section, we present the Ehrenfeucht-Fraïssé game and briefly sketch a proof that the Crane Beach conjecture holds for FO 2 m [<, +1].  ... 
arXiv:1507.05175v2 fatcat:tcwgzerg3bca3lqpfim6a4nlxi

Graded modal logic and counting bisimulation [article]

Martin Otto
2019 arXiv   pre-print
Lemma 1.3 (graded modal Ehrenfeucht-Fraïssé theorem).  ...  Recall how the classical Ehrenfeucht-Fraïssé matches m-isomorphy, i.e. m-round pebble game b&f equivalence, with m-elemenatry equivalence.  ...  The proof is again by a standard b&f argument about the classical q-round Ehrenfeucht-Fraïssé game for FO to establish ≃ q . Lemma 2.4.  ... 
arXiv:1910.00039v1 fatcat:v7htrysqvbep7kx7ayxdtnytte

JAAKKO HINTIKKA 1929–2015

JOUKO VÄÄNÄNEN
2015 Bulletin of Symbolic Logic  
. , x n ) in a model M and b 1 , . . . , b n satisfy C m,n i (x 1 , . . . , x n ) in a model N , then C m,n i (x 1 , . . . , x n ) codes a winning strategy for player II in the m-move Ehrenfeucht-Fraïssé-game  ...  A similar analysis of predicate logic was introduced by Fraïssé [6] in terms of back-and-forth systems, and by Ehrenfeucht [5] in game-theoretic terms.  ... 
doi:10.1017/bsl.2015.35 fatcat:vwqjwmv4knfr5dzxkx7nm76pva

JSL volume 80 issue 1 Cover and Front matter

2015 Journal of Symbolic Logic (JSL)  
strategies in long Ehrenfeucht-Fraïssé games, by S.  ...  .................................... 234 Large cardinals and lightface defi nable well-orders, without the GCH, by SY-DAVID FRIEDMAN, PETER HOLY, and PHILIPP LÜCKE ............................... 251 Positional  ... 
doi:10.1017/jsl.2014.12 fatcat:hbnu4qhvdng3zaar6ffw7fmyqe

On Finding a First-Order Sentence Consistent with a Sample of Strings

Thiago Alves Rocha, Ana Teresa Martins, Francicleber Martins Ferreira
2018 Electronic Proceedings in Theoretical Computer Science  
We use results of the Ehrenfeucht-Fra\"iss\'e game over successor string structures in order to design an algorithm to find such sentence.  ...  We use conditions characterizing the winning strategies for the Spoiler on successor strings structures in order to define formulas which distinguish two strings.  ...  Ehrenfeucht-Fraïssé games (EF games) [5] is a fundamental technique in finite model theory [3, 6] in proving the inexpressibility of certain properties in first-order logic.  ... 
doi:10.4204/eptcs.277.16 fatcat:24ctnzgzrfbjfallwbzx6v4l2a

On the Lengths of Symmetry Breaking-Preserving Games on Graphs [article]

Frank Harary, Wolfgang Slany, Oleg Verbitsky
2004 arXiv   pre-print
Given a graph G, we consider a game where two players, A and B, alternatingly color edges of G in red and in blue respectively.  ...  The lower bound is based on relations with Ehrenfeucht games from model theory. We also consider complete graphs and prove that l(K_n)=O(1).  ...  Acknowledgement We thank Helmut Veith for helpful discussions on the Ehrenfeucht-Fraïssé games, Oleg Pikhurko for useful comments on the paper, and an anonymous referee for a considerable simplification  ... 
arXiv:math/0401363v1 fatcat:6oyjsvtfnnbjxfdht4r2dqgwrm

FO Model Checking of Interval Graphs [chapter]

Robert Ganian, Petr Hliněný, Daniel Král', Jan Obdržálek, Jarett Schwartz, Jakub Teska
2013 Lecture Notes in Computer Science  
The main positive result is that this problem can be solved in time O(n log n) for n-vertex interval graphs with representations containing only intervals with lengths from a prescribed finite set.  ...  We complement this result by showing that the same is not true if the lengths are restricted to any set that is dense in some open subset, e.g., in the set (1, 1 + ε).  ...  -The duplicator wins the d-round Ehrenfeucht-Fraïssé game for R and R . Lemma 4 . 1 . 41 Let L be a finite set of positive rational numbers.  ... 
doi:10.1007/978-3-642-39212-2_24 fatcat:u2gpiff3tngejl5dqp2lqhdnqy

Weak Ehrenfeucht-Fraïssé games

Tapani Hyttinen, Vadim Kulikov
2011 Transactions of the American Mathematical Society  
Thus the difference between this and the ordinary Ehrenfeucht-Fraïssé game is that the isomorphism can be arbitrary, whereas in the ordinary EF-game it is determined by the moves of the players.  ...  In this paper we define a game which is played between two players I and II and two mathematical structures A and B.  ...  Winning strategies in various Ehrenfeucht-Fraïssé games provide such invariants.  ... 
doi:10.1090/s0002-9947-2011-05222-0 fatcat:xshduwvfknhahicyfm56tt5mpy

Games, equations and the dot-depth hierarchy

F. Blanchet-Sadri
1989 Computers and Mathematics with Applications  
Those are then generalized to definitions of equation systems satisfied in monoid varieties of higher sublevels. A version of the Ehrenfeueht-Fraisse game is used to verify equations.  ...  LOWER BOUNDS ON DOT-DEPTH In this section, Ehrenfeucht-Fraisse games are used to prove lower bounds on a language's complexity through equtions.  ...  The standard Ehrenfeucht-Fraisse game is the special case of (M(U, V), where r~ = (1 ..... 1). For a detailed discussion, cf. Rosenstein [23] or Fraisse [24] .  ... 
doi:10.1016/0898-1221(89)90179-x fatcat:px6cx5qu25dzzfv2ay4mrzvrp4

Cayley structures and common knowledge [article]

Felix Canavoi, Martin Otto
2021 arXiv   pre-print
We investigate multi-agent epistemic modal logic with common knowledge modalities for groups of agents and obtain van Benthem style model-theoretic characterisations, in terms of bisimulation invariance  ...  We are particularly indebted to an anonymous referee whose attention to detail, insightful corrections and suggestions have led to essential improvements in this revision.  ...  But in order to win the Ehrenfeucht-Fraïssé game we need to be able to ensure that a response in a given round of the game can match long paths with long paths.  ... 
arXiv:1909.11521v4 fatcat:ufrp2i57gfc4ppcf6hlxiuvuou
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