On the Strong Freese-Nation Property

On the Strong Freese-Nation Property

We show that there is a boolean algebra that has the Freese-Nation property (FN) but not the strong Freese-Nation property (SFN), thus answering a question of Heindorf and Shapiro. Along the way, we produce some new characterizations of the FN and SFN in terms of sequences of elementary submodels.

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Veröffentlicht in:Order (Dordrecht) 2017-03, Vol.34 (1), p.91-111
1. Verfasser: Milovich, David
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Boolean algebra
Discrete Mathematics
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
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Zusammenfassung:We show that there is a boolean algebra that has the Freese-Nation property (FN) but not the strong Freese-Nation property (SFN), thus answering a question of Heindorf and Shapiro. Along the way, we produce some new characterizations of the FN and SFN in terms of sequences of elementary submodels.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-016-9389-9