Almost free groups and Ehrenfeucht-Fra\"ıssé games for successors of singular cardinals

Details Almost free groups and Ehrenfeucht-Fra\"ıssé games for successors of singular cardinals Almost free groups and Ehrenfeucht-Fra\"ıssé games for successors of singular cardinals

2002-12-04

arxiv.org/abs/math/0212063v1

Mathematics

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Scientific paper

We strengthen non-structure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraisse 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*omega_1)-game-free groups of cardinality lambda. We concentrate on successors of singular cardinals.

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