English

The automorphism group of a saturated model has a large dense free subgroup

Logic 2008-02-03 v1

Abstract

We prove that for a stable theory T,T, if MM is a saturated model of TT of cardinality λ\lambda where λ>T,\lambda > \big|T\big|, then Aut(M)Aut(M) has a dense free subgroup on 2λ2^{\lambda} generators. This affirms a conjecture of Hodges.

Keywords

Cite

@article{arxiv.math/9304201,
  title  = {The automorphism group of a saturated model has a large dense free subgroup},
  author = {Garvin Melles and Saharon Shelah},
  journal= {arXiv preprint arXiv:math/9304201},
  year   = {2008}
}