Almost free groups and Ehrenfeucht–Fraı̈ssé games for successors of singular cardinals

Saharon Shelah, Pauli Väisänen
2002 Annals of Pure and Applied Logic  
We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fra ssà e games between a ÿxed group of cardinality and a free Abelian group. A group is called -game-free if the isomorphism player has a winning strategy in the game (of the described form) of length ∈ . We prove for a large set of successor cardinals = + the existence of nonfree ( · !1)-game-free groups of cardinality . We concentrate on successors of singular cardinals. (S. Shelah), pauli.vaisanen@helsinki.ÿ (P. V ais anen).
doi:10.1016/s0168-0072(02)00037-4 fatcat:upvdjksw7rg7jhuh5btpf5h3by