Positional Strategies in long Ehrenfeucht-Fra{\"{i}}ss\'e games

by Shelah and Vaananen and Velickovic. [ShVaVe:1034]
J Symbolic Logic, 2015
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{i}sse-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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