Partial orderings with the weak Freese-Nation property

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Annals of Pure and Applied Logic 80 (1):35-54 (1996)
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Abstract

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, every ccc complete Boolean algebra has this property while, under b 2, there exists no complete Boolean algebra with the WFN

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10.1016/0168-0072(95)00047-x

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Citations of this work

On the weak Freese–Nation property of ?(ω).Sakaé Fuchino, Stefan Geschke & Lajos Soukupe - 2001 - Archive for Mathematical Logic 40 (6):425-435.
Almost disjoint families and diagonalizations of length continuum.Dilip Raghavan - 2010 - Bulletin of Symbolic Logic 16 (2):240 - 260.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
On L∞κ-free Boolean algebras.Sakaé Fuchino, Sabine Koppelberg & Makoto Takahashi - 1992 - Annals of Pure and Applied Logic 55 (3):265-284.
Some remarks on openly generated Boolean algebras.Sakaé Fuchino - 1994 - Journal of Symbolic Logic 59 (1):302-310.
Strong analogues of Martin's axiom imply axiom R.Robert E. Beaudoin - 1987 - Journal of Symbolic Logic 52 (1):216-218.

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