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Positional strategies in long Ehrenfeucht-Fraissé games

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 ω_1 but there is no σ-closed back-and-forth set for the two models. If CH fails, no such pairs of models exist.

preprint2013arXivOpen access
Saharon ShelahJouko VäänänenBoban Velickovic
math.LO
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Open access3 authors1 topic
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Saharon ShelahJouko VäänänenBoban Velickovic

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