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)

@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},
 mrnumber = {1934121},
 mrclass = {03E05 (03C75 20K20)},
 doi = {10.1016/S0168-0072(02)00037-4},
 note = {\href{https://arxiv.org/abs/math/0212063}{arXiv: math/0212063}},
 arxiv_number = {math/0212063}
}