Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals

  title={Almost free groups and Ehrenfeucht-Fra{\"i}ss{\'e} games for successors of singular cardinals},
  author={Saharon Shelah and Pauli V{\"a}is{\"a}nen},
  journal={Ann. Pure Appl. Log.},
  • Saharon Shelah, Pauli Väisänen
  • Published 2002
  • Computer Science, Mathematics
  • Ann. Pure Appl. Log.
  • Abstract We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht–Fraisse games between a fixed group of cardinality λ and a free Abelian group. A group is called e -game-free if the isomorphism player has a winning strategy in the game (of the described form) of length e ∈ λ . We prove for a large set of successor cardinals λ = μ + the existence of nonfree ( μ · ω 1 )-game-free groups of cardinality λ . We concentrate on successors of singular cardinals.