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Page 5727 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
A group G is said to be e-game-free if the isomorphism player has a winning strategy in the Ehrenfeucht-Fraiss¢é game of length e« between G and a free group, with countably many elements chosen at each  ...  Stoyan Nedev (BG-AOS; Sofia) 2003h:03073 03E05 03C75 20K20 Shelah, Saharon (IL-HEBR-IM; Jerusalem) ; Vaisinen, Pauli (FIN-HELS; Helsinki) Almost free groups and Ehrenfeucht-Fraissé games for successors  ... 

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.  ...  Fraïssé introduced back-and-forth systems and what we call the Ehrenfeucht-Fraïssé games.  ... 
doi:10.1090/s0002-9947-2011-05222-0 fatcat:xshduwvfknhahicyfm56tt5mpy

Games and elementary equivalence of II1-factors

Isaac Goldbring, Thomas Sinclair
2015 Pacific Journal of Mathematics  
We use Ehrenfeucht-Fraïssé games to give a local geometric criterion for elementary equivalence of II_1 factors.  ...  We obtain as a corollary that two II_1 factors are elementarily equivalent if and only their unitary groups are elementarily equivalent as Z_4-metric spaces.  ...  Ehrenfeucht-Fraïssé games have long been a tool in model theory for establishing that structures are elementarily equivalent.  ... 
doi:10.2140/pjm.2015.278.103 fatcat:76e47hz2qnhldjchn25hjr7mtu

Reflections on Finite Model Theory

Phokion G. Kolaitis
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
Reinforces the unity of computation and logic. Yields machine-independent characterizations of computational complexity classes.  ...  Main Finding: All major computational complexity classes, including P, NP, and PSPACE, can be characterized in terms of definability in various logics on classes of finite structures.  ...  -Fraïssé games and their variants: Ehrenfeucht -Fraïssé games for ESO, pebble games, and games for logics with generalized quantifiers.However, Chandra and Harel's Problem and Gurevich's Conjecture remain  ... 
doi:10.1109/lics.2007.39 dblp:conf/lics/Kolaitis07 fatcat:3eulyaqcgbfdzihya6kzjxm2ru

Games and Trees in Infinitary Logic: A Survey [chapter]

Jouko Väänänen
1995 Quantifiers: Logics, Models and Computation  
The central idea is to use trees and Ehrenfeucht-Fraïssé games to measure differences between uncountable models.  ...  We describe the work and underlying ideas of the Helsinki Logic Group in infinitary logic.  ...  We can go a long way by studying Ehrenfeucht-Fraïssé-games only.  ... 
doi:10.1007/978-94-017-0522-6_5 fatcat:y3qrbhghjfdqve76vz2ebvcsgu

Page 7599 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
{For the entire collection see MR 2004f:20002. } 2004j:03047 03C60 03C05 03E35 03E55 20K99 Viaisinen, Pauli (FIN-HELS; Helsinki) Almost free groups and long Ehrenfeucht-Fraissé games.  ...  If « is an infinite cardinal, then a group G is called «-game- free iff there is a free-abelian group F such that in the canon- For the web version of Mathematical Reviews, see http: //www.ams.org/mathscinet  ... 

Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals [article]

Saharon Shelah, Pauli Väisänen
2002 arXiv   pre-print
We strengthen non-structure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraisse games between a fixed group of cardinality lambda and a free Abelian group.  ...  A group is called epsilon-game-free if the isomorphism player has a winning strategy in the game (of the described form) of length epsilon in lambda.  ...  For an ordinal ǫ, a group G is called ǫ-game-free, if the "isomorphism player" has a winning strategy in the Ehrenfeucht-Fraïssé game of length ǫ between G and a free Abelian group (countable many elements  ... 
arXiv:math/0212063v1 fatcat:ozvuznpggbejtnzadwajefjfii

Expressive completeness through logically tractable models

Martin Otto
2013 Annals of Pure and Applied Logic  
based equivalences in hypergraphs and relational structures.  ...  the use and availability of tractable representatives in the relevant model classes.  ...  I am grateful for discussions with Vince Bárány and Balder ten Cate concerning the guarded negation fragment.  ... 
doi:10.1016/j.apal.2013.06.017 fatcat:cj5cxfl2afhanouwu6l44j5z3m

Page 6909 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
Here N =; M means that in a certain Ehrenfeucht-Fraissé game between N and M, depending on ¢ and A, the player 3 has a winning strategy.  ...  More exactly, they show it in the presence of infinitely many automorphisms, and then use a result of Zoe Chatzidakis on extensions of free groups of automorphisms in a stable context to prove the finite  ... 

From Hilbert's program to a logic tool box

J. A. Makowsky
2008 Annals of Mathematics and Artificial Intelligence  
In this paper I discuss what, according to my long experience, every computer scientists should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction.  ...  For Witek Marek, first mentor, then colleague and true friend, on the occasion of his 65th birthday.  ...  Halevy and D. Hay for stimulating discussions and suggestions about how to teach Logic to Computer Science students. I would like to thank the editors of this volume, M. Kaminski and M.  ... 
doi:10.1007/s10472-009-9115-z fatcat:5czgb6guqzb3hdq46spqz24wdy

Almost free groups and Ehrenfeucht–Fraı̈ssé games for successors of singular cardinals

Saharon Shelah, Pauli Väisänen
2002 Annals of Pure and Applied Logic  
We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fra ssà e games between a ÿxed group of cardinality and a free Abelian group.  ...  A group is called -game-free if the isomorphism player has a winning strategy in the game (of the described form) of length ∈ .  ...  Introduction The problem of possible cardinals carrying a nonfree almost free Abelian group has already a long history, see e.g. [3] .  ... 
doi:10.1016/s0168-0072(02)00037-4 fatcat:upvdjksw7rg7jhuh5btpf5h3by

On Invariants for ω 1 -Separable Groups

Paul C. Eklof, Matthew Foreman, Saharon Shelah
1995 Transactions of the American Mathematical Society  
We study the classification of ω 1 -separable groups using Ehrenfeucht-Fraïssé games and prove a strong classification result assuming PFA, and a strong non-structure theorem assuming ♦. 1991 Mathematics  ...  It is our aim here to use the methodology of the Helsinki school -which involves Ehrenfeucht-Fraïssé games (cf.  ...  We begin by describing the Ehrenfeucht-Fraïssé (or EF) games, after which we can state our results more precisely.  ... 
doi:10.2307/2155042 fatcat:32hmaepqd5colhmwv4wo35u2cm

On invariants for omega_1-separable groups [article]

Paul C. Eklof, Matthew Foreman, Saharon Shelah
1995 arXiv   pre-print
We study the classification of omega_1-separable groups using Ehrenfeucht-Fraisse games and prove a strong classification result assuming PFA, and a strong non-structure theorem assuming diamond.  ...  It is our aim here to use the methodology of the Helsinki school -which involves Ehrenfeucht-Fraïssé games (cf.  ...  We begin by describing the Ehrenfeucht-Fraïssé (or EF) games, after which we can state our results more precisely.  ... 
arXiv:math/9501223v1 fatcat:ig35536guvd3bj7g3t7lyrz3bu

An Ehrenfeucht-Fraisse Game Approach to Collapse Results in Database Theory [article]

Nicole Schweikardt
2002 arXiv   pre-print
We present a new Ehrenfeucht-Fraisse game approach to collapse results in database theory and we show that, in principle, this approach suffices to prove every natural generic collapse result.  ...  This, as a side product, also leads to an Ehrenfeucht-Fraisse game proof of the theorem of Ginsburg and Spanier, stating that the spectra of FO(<,+)-sentences are semi-linear.  ...  Acknowledgements: I want to thank Clemens Lautemann for his guidance and for many valuable discussions and suggestions concerning the research presented in this paper.  ... 
arXiv:cs/0212049v1 fatcat:slxlikn3d5cfnchbd5vbh3xogm

The canary tree [article]

Alan H. Mekler, Saharon Shelah
1993 arXiv   pre-print
The Canary Tree and Ehrenfeucht-Fraïssé Games A central idea in the Helsinki school's approach to finding an analogy at ω 1 of the theory of L ∞ω is the notion of an Ehrenfeucht-Fraïssé game of length  ...  However for some natural structures such as free groups (or free abelian groups) or ω 1 -like dense linear orders the existence of a universal non-equivalence tree of cardinality 2 ℵ 0 is equivalent to  ... 
arXiv:math/9308210v1 fatcat:fp6glbecuzbofcm37uqmgcsjle
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