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Displaying similar documents to “On the relationship between projective distributive lattices and Boolean algebras.”

Openly generated Boolean algebras and the Fodor-type reflection principle

Sakaé Fuchino, Assaf Rinot (2011)

Fundamenta Mathematicae

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We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is ℵ₂-projective. Previously it was known that this characterization of openly generated Boolean algebras follows from Axiom R. Since FRP is preserved by c.c.c. generic extension, we conclude in particular that this characterization is consistent with any set-theoretic assertion forcable by a c.c.c. poset starting from a model of FRP. A...

Boolean algebras admitting a countable minimally acting group

Aleksander Błaszczyk, Andrzej Kucharski, Sławomir Turek (2014)

Open Mathematics

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The aim of this paper is to show that every infinite Boolean algebra which admits a countable minimally acting group contains a dense projective subalgebra.

Zero-dimensional Dugundji spaces admit profinite lattice structures

Lutz Heindorf (1992)

Commentationes Mathematicae Universitatis Carolinae

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We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.