Boolean algebras with prescribed topological densities

L. Soukup

The topological density $ \operatorname{d}(B)$ of a Boolean algebra $ B$ is the minimal cardinal $ {\mu}$ such that $ B\setminus \{0_B\}$ can be covered by $ {\mu}$ ultrafilters.

We give a simplified proof of a theorem of M. Rabus and S. Shelah claiming that for each cardinal $ {\mu}$ there is a c.c.c Boolean algebra $ {\mathcal B}$ with topological density $ {\mu}$.

M. Rabus, S. Shelah, Topological density of ccc Boolean algebras - every cardinality occurs, Proc. Am. Math. Soc. Vol 127 (1999). No 9. pp. 2573-2581.

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