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Page 5727 of Mathematical Reviews Vol. , Issue 2003h
[page]
2003
Mathematical Reviews
Preserved Fulltext
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
2011
Transactions of the American Mathematical Society
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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
2015
Pacific Journal of Mathematics
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2014 pre-print arXiv:1406.5242v1 fatcat:ehsx65gvwjdl3pcedmqxosfkgiOther Versions
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
2007
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
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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]
1995
Quantifiers: Logics, Models and Computation
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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
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{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]
2002
arXiv
pre-print
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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
2013
Annals of Pure and Applied Logic
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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
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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
2008
Annals of Mathematics and Artificial Intelligence
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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
2002
Annals of Pure and Applied Logic
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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
1995
Transactions of the American Mathematical Society
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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]
1995
arXiv
pre-print
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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]
2002
arXiv
pre-print
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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]
1993
arXiv
pre-print
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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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