# Sh:549

- Fuchino, S., Koppelberg, S., & Shelah, S. (1996).
*Partial orderings with the weak Freese-Nation property*. Ann. Pure Appl. Logic,**80**(1), 35–54. arXiv: math/9508220 DOI: 10.1016/0168-0072(95)00047-X MR: 1395682 -
Abstract:

A partial ordering P is said to have the weak Freese-Nation property (WFN) if there is a mapping f:P\longrightarrow [P]^{\leq\aleph_0} such that, for any a, b\in P, if a\leq b then there exists c\in f(a)\cap f(b) such that a\leq c\leq 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 {\bf b}\geq\aleph_2, there exists no cBA with the WFN. - Version 1995-08-25_10 (24p) published version (20p)

Bib entry

@article{Sh:549, author = {Fuchino, Saka{\'e} and Koppelberg, Sabine and Shelah, Saharon}, title = {{Partial orderings with the weak Freese-Nation property}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {80}, number = {1}, year = {1996}, pages = {35--54}, issn = {0168-0072}, mrnumber = {1395682}, mrclass = {03G05 (06A07 06E05)}, doi = {10.1016/0168-0072(95)00047-X}, note = {\href{https://arxiv.org/abs/math/9508220}{arXiv: math/9508220}}, arxiv_number = {math/9508220} }