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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 ...##
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Weak Ehrenfeucht-Fraïssé games

2011
*
Transactions of the American Mathematical Society
*

Thus the difference between this

doi:10.1090/s0002-9947-2011-05222-0
fatcat:xshduwvfknhahicyfm56tt5mpy
*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*. ...##
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Games and elementary equivalence of II1-factors

2015
*
Pacific Journal of Mathematics
*

We use

doi:10.2140/pjm.2015.278.103
fatcat:76e47hz2qnhldjchn25hjr7mtu
*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. ...##
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Reflections on Finite Model Theory

2007
*
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
*

Reinforces the unity of computation

doi:10.1109/lics.2007.39
dblp:conf/lics/Kolaitis07
fatcat:3eulyaqcgbfdzihya6kzjxm2ru
*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 ...##
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Games and Trees in Infinitary Logic: A Survey
[chapter]

1995
*
Quantifiers: Logics, Models and Computation
*

The central idea is to use trees

doi:10.1007/978-94-017-0522-6_5
fatcat:y3qrbhghjfdqve76vz2ebvcsgu
*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. ...##
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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 ...##
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Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals
[article]

2002
*
arXiv
*
pre-print

We strengthen non-structure theorems for

arXiv:math/0212063v1
fatcat:ozvuznpggbejtnzadwajefjfii
*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 ...##
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Expressive completeness through logically tractable models

2013
*
Annals of Pure and Applied Logic
*

based equivalences in hypergraphs

doi:10.1016/j.apal.2013.06.017
fatcat:cj5cxfl2afhanouwu6l44j5z3m
*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. ...##
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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 ...##
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From Hilbert's program to a logic tool box

2008
*
Annals of Mathematics and Artificial Intelligence
*

In this paper I discuss what, according to my

doi:10.1007/s10472-009-9115-z
fatcat:5czgb6guqzb3hdq46spqz24wdy
*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. ...##
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Almost free groups and Ehrenfeucht–Fraı̈ssé games for successors of singular cardinals

2002
*
Annals of Pure and Applied Logic
*

We strengthen nonstructure theorems for

doi:10.1016/s0168-0072(02)00037-4
fatcat:upvdjksw7rg7jhuh5btpf5h3by
*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] . ...##
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On Invariants for ω 1 -Separable Groups

1995
*
Transactions of the American Mathematical Society
*

We study the classification of ω 1 -separable

doi:10.2307/2155042
fatcat:32hmaepqd5colhmwv4wo35u2cm
*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. ...##
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On invariants for omega_1-separable groups
[article]

1995
*
arXiv
*
pre-print

We study the classification of omega_1-separable

arXiv:math/9501223v1
fatcat:ig35536guvd3bj7g3t7lyrz3bu
*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. ...##
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An Ehrenfeucht-Fraisse Game Approach to Collapse Results in Database Theory
[article]

2002
*
arXiv
*
pre-print

We present a new

arXiv:cs/0212049v1
fatcat:slxlikn3d5cfnchbd5vbh3xogm
*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. ...##
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The canary tree
[article]

1993
*
arXiv
*
pre-print

The Canary Tree

arXiv:math/9308210v1
fatcat:fp6glbecuzbofcm37uqmgcsjle
*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 ...
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