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Some remarks on openly generated Boolean algebras

Journal of Symbolic Logic 59 (1):302-310 (1994)

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Partial orderings with the weak Freese-Nation property.Sakaé Fuchino, Sabine Koppelberg & Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (1):35-54.details A partial ordering P is said to have the weak Freese-Nation property if there is a mapping tf : P → [P]0 such that, for any a, b ε P, if a b then there exists c ε tf∩tf such that a c b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g. under CH, (...) Download Export citation Bookmark 3 citations
Semi-Cohen Boolean algebras.Bohuslav Balcar, Thomas Jech & Jindřich Zapletal - 1997 - Annals of Pure and Applied Logic 87 (3):187-208.details We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion. Download Export citation Bookmark 4 citations

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