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.
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