English

Positional strategies in long Ehrenfeucht-Fraiss\'e games

Logic 2013-08-02 v1

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-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.

Keywords

Cite

@article{arxiv.1308.0156,
  title  = {Positional strategies in long Ehrenfeucht-Fraiss\'e games},
  author = {Saharon Shelah and Jouko Väänänen and Boban Velickovic},
  journal= {arXiv preprint arXiv:1308.0156},
  year   = {2013}
}