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}
}