Abstract

It is shown to be consistent with 2 ℵ 0 > ℵ 1 {2^{{\aleph _0}}} > {\aleph _1} that the smallest ℵ 2 {\aleph _2} -complete Boolean subalgebra of P ( R ) \mathcal {P}({\mathbf {R}}) containing all closed sets is P ( R ) \mathcal {P}({\mathbf {R}}) . Some related results are also proved.

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