### 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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