Almost free groups and EhrenfeuchtFra\"ıssé games for successors of singular cardinals
Abstract
We strengthen nonstructure theorems for almost free Abelian groups by studying long EhrenfeuchtFraisse games between a fixed group of cardinality lambda and a free Abelian group. A group is called epsilongamefree 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)gamefree groups of cardinality lambda. We concentrate on successors of singular cardinals.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2002
 arXiv:
 arXiv:math/0212063
 Bibcode:
 2002math.....12063S
 Keywords:

 Mathematics  Logic;
 Mathematics  Group Theory