# 2008 seminar talk: Measurable cardinals and the Cofinality of the Symmetric Group

Talk held by Lyubomyr Zdomskyy (KGRC) at the KGRC seminar on 2008-11-06.

### Abstract

Assuming the existence of a hypermeasurable cardinal, we shall
construct a model of Set Theory with a measurable cardinal
$kappa$ such that $2^kappa=kappa^++$ and the group $Sym(kappa)$ of all
permutations of $kappa$ cannot be written as a union of a chain of
proper subgroups of length $<kappa^++$. The proof involves
the iteration of a suitably defined uncountable version of the
Miller forcing poset as well as the ``tuning fork* argument introduced
by S.D. Friedman and K. Thompson.
*

Based on the joint work with S.D. Friedman