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

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.