# Sh:787

- Shelah, S., & Väisänen, P. (2002).
*Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals*. Ann. Pure Appl. Logic,**118**(1-2), 147–173. arXiv: math/0212063 DOI: 10.1016/S0168-0072(02)00037-4 MR: 1934121 -
Abstract:

We strengthen non-structure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraı̈ssé games between a fixed group of cardinality \lambda and a free Abelian group. A group is called \epsilon-game-free if the isomorphism player has a winning strategy in the game (of the described form) of length \epsilon \in \lambda. We prove for a large set of successor cardinals \lambda = \mu^+ existence of nonfree (\mu \cdot \omega_1)-game-free groups of cardinality \lambda. We concentrate on successors of singular cardinals. - published version (27p)

Bib entry

@article{Sh:787, author = {Shelah, Saharon and V{\"a}is{\"a}nen, Pauli}, title = {{Almost free groups and Ehrenfeucht-Fra\"iss\'e games for successors of singular cardinals}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {118}, number = {1-2}, year = {2002}, pages = {147--173}, issn = {0168-0072}, doi = {10.1016/S0168-0072(02)00037-4}, mrclass = {03E05 (03C75 20K20)}, mrnumber = {1934121}, mrreviewer = {O. V. Belegradek}, doi = {10.1016/S0168-0072(02)00037-4}, note = {\href{https://arxiv.org/abs/math/0212063}{arXiv: math/0212063}}, arxiv_number = {math/0212063} }