# Sh:1034

• Shelah, S., Veličković, B., & Väänänen, J. A. (2015). Positional strategies in long Ehrenfeucht-Fraïssé games. J. Symb. Log., 80(1), 285–300.
• Abstract:
We prove that it is relatively consistent with {\rm ZF + CH} that there exist two models of cardinality \aleph_2 such that the second player has a winning strategy in the Ehrenfeucht-Fraı̈ssé-game of length \omega_1 but there is no \sigma-closed back-and-forth set for the two models. If {\rm CH} fails, no such pairs of models exist.
• published version (16p)
Bib entry
@article{Sh:1034,
author = {Shelah, Saharon and Veli{\v{c}}kovi{\'c}, Boban and V{\"a}{\"a}n{\"a}nen, Jouko A.},
title = {{Positional strategies in long Ehrenfeucht-Fra\"iss\'e games}},
journal = {J. Symb. Log.},
fjournal = {The Journal of Symbolic Logic},
volume = {80},
number = {1},
year = {2015},
pages = {285--300},
issn = {0022-4812},
mrnumber = {3320594},
mrclass = {03E35 (03C55 03E10)},
doi = {10.1017/jsl.2014.43},
note = {\href{https://arxiv.org/abs/1308.0156}{arXiv: 1308.0156}},
arxiv_number = {1308.0156}
}