Partial orderings with the weak Freese-Nation property

Details Partial orderings with the weak Freese-Nation property Partial orderings with the weak Freese-Nation property

1995-08-15

arxiv.org/abs/math/9508220v1

Ann. Pure Appl. Logic 80 (1996), 35--54

Mathematics

Logic

Scientific paper

A partial ordering P is said to have the weak Freese-Nation property (WFN) if there is a mapping f:P ---> [P]^{<= aleph_0} such that, for any a, b in P, if a <= b then there exists c in f(a) cap f(b) such that a <= c <= b. In this note, we study the WFN and some of its generalizations. Some features of the class of BAs with the WFN seem to be quite sensitive to additional axioms of set theory: e.g., under CH, every ccc cBA has this property while, under b >= aleph_2, there exists no cBA with the WFN.

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