### 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.

Back to the list of publications