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 \(\mathsf{Aut}(S_\infty/fin)\), analogous to the well known results by Rudin, Shelah and Velickovic about \(\mathsf{Aut}(P(\omega)/fin)\). 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.
Automorphisms of S_infty/fin
23.10.2008 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25