Power set modulo small, the singular of uncountable cofinality

Abstract

Let mu be singular of uncountable cofinality. If mu>2^{cf(mu)}, we prove that in P=([mu]^mu,supseteq) as a forcing notion we have a natural complete embedding of Levy(aleph_0, mu^+) (so P collapses mu^+ to aleph_0) and even Levy(aleph_0, U_{J^{bd}_kappa}(mu)) . The ``natural&#39;&#39; means that the forcing ({p in [mu]^mu :p closed}, supseteq) is naturally embedded and is equivalent to the Levy algebra. If mu <2^{cf(mu)} we have weaker results.