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POSITIONAL STRATEGIES IN LONG EHRENFEUCHT–FRAÏSSÉ GAMES

Published online by Cambridge University Press:  13 March 2015

S. SHELAH
Affiliation:
INSTITUTE OF MATHEMATICS, HEBREW UNIVERSITY, JERUSALEM ISRAEL AND DEPARTMENT OF MATHEMATICS, RUTGERS UNIVERSITY, NEW BRUNSWICK, NJ, USAE-mail: shelah@math.huji.ac.ilURL: http://shelah.logic.at
J. VÄÄNÄNEN
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS, UNIVERSITY OF HELSINKI, FINLAND AND INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITY OF AMSTERDAM, THE NETHERLANDSE-mail: jouko.vaananen@helsinki.fiURL: http://www.math.helsinki.fi/logic/people/jouko.vaananen
B. VELIČKOVIĆ
Affiliation:
EQUIPE DE LOGIQUE MATHÉMATIQUE, INSTITUT DE MATHÉMATIQUES DE JUSSIEU, UNIVERSITÉ PARIS DIDEROT, PARIS, FRANCEE-mail: boban@math.univ-paris-diderot.frURL: http://www.logique.jussieu.fr/∼boban

Abstract

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–Fraïssé-game of length ω1 but there is no σ-closed back-and-forth set for the two models. If CH fails, no such pairs of models exist.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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