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'' 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.
Categories: math.LO