2013/08/01 by Saharon Shelah, Shelah, Saharon, Jouko Väänánen +5
Computer Science · Economics, Econometrics and Finance · Mathematics · #03Bxx #03Exx #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Economic theories and models #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03Bxx #msc:03Exx
paper · pdf · doi:10.48550/arxiv.1308.0156
published as J. Symb. Log. 80 No. 1 (2015) 285--300
arxiv created 2013/08/01 · openalex publication_date 2013/08/01 · arxiv updated 2013/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that it is relatively consistent with ZF + CH that there exist two models of cardinality ℵ2 such that the second player has a winning strategy in the Ehrenfeucht-Fraïssé-game of length ω1 but there is no σ-closed back-and-forth set for the two models. If CH fails, no such pairs of models exist.