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POSITIONAL STRATEGIES IN LONG EHRENFEUCHT–FRAÏSSÉ GAMES
Published online by Cambridge University Press: 13 March 2015
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.
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- Copyright © The Association for Symbolic Logic 2015