Partial orderings with the weak Freese-Nation property

Sakaé Fuchino*, Sabine Koppelberg, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

A partial ordering P is said to have the weak Freese-Nation property (WFN) if there is a mapping f : P → [P] ≤א0 such that, for any a, b ∈ P, if a ≤ b then there exists c ∈ f(a)∩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 Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g. under CH, every ccc complete Boolean algebra has this property while, under b ≥ א2, there exists no complete Boolean algebra with the WFN (Theorem 6.2).

Original languageEnglish
Pages (from-to)35-54
Number of pages20
JournalAnnals of Pure and Applied Logic
Volume80
Issue number1
DOIs
StatePublished - 15 Jul 1996

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