Positional strategies in long Ehrenfeucht-Fraiss\'e games
classification
🧮 math.LO
keywords
modelsexisttherealephback-and-forthcardinalityconsistente-game
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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-Fra\"iss\'e-game of length \omega_1 but there is no \sigma-closed back-and-forth set for the two models. If CH fails, no such pairs of models exist.
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