Kurt Gödel Research Center

2008 seminar talk: Automorphisms of S_infty/fin

Talk held by Asger Törnquist (KGRC) at the KGRC seminar on 2008-10-23.

Abstract

Let S_infty be the full permutation group on \omega and let fin denote the (normal) subgroup of permutations that act identically on a co-finite set. In this talk I will discuss some results about the structure of Aut(S_\infty/fin), analogous to the well known results by Rudin, Shelah and Velickovic about Aut(P(\omega)/fin). Specifically, I will show that all "definable" automorphisms are implemented by a bijection between co-finite sets, but that CH allows us to construct one that is not.