# Sh:1034

- Shelah, S., Veličković, B., & Väänänen, J. A. (2015).
*Positional strategies in long Ehrenfeucht-Fraïssé games*. J. Symb. Log.,**80**(1), 285–300. arXiv: 1308.0156 DOI: 10.1017/jsl.2014.43 MR: 3320594 -
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} }