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POSITIONAL STRATEGIES IN LONG EHRENFEUCHT–FRAÏSSÉ GAMES

  • S. SHELAH (a1) (a2), J. VÄÄNÄNEN (a3) and B. VELIČKOVIĆ (a4)

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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