Power set modulo small, the singular of uncountable cofinality

by Shelah. [Sh:861]
J Symbolic Logic, 2007
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.


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