Journal of Symbolic Logic 59 (1):302-310 (1994)

A Boolean algebra B is said to be openly generated if {A: A ≤rc B, |A| = ℵ0} includes a club subset of [ B]ℵ0 . We show: (V = L). For any cardinal κ there exists an L∞κ-free Boolean algebra which is not openly generated (Proposition 4.1). (MA+(σ-closed)). Every L∞ℵa -free Boolean algebra is openly generated (Theorem 4.2). The last assertion follows from a characterization of openly generated Boolean algebras under MA+(σ-closed) (Theorem 3.1). Using this characterization we also prove the independence of problem 7 in Scepin [15] (Proposition 4.3 and Theorem 4.4)
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275267
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 62,289
Through your library

References found in this work BETA

On L∞Κ-Free Boolean Algebras.Sakaé Fuchino, Sabine Koppelberg & Makoto Takahashi - 1992 - Annals of Pure and Applied Logic 55 (3):265-284.
On Potential Embedding and Versions of Martin's Axiom.Sakaé Fuchino - 1992 - Notre Dame Journal of Formal Logic 33 (4):481-492.

Add more references

Citations of this work BETA

Semi-Cohen Boolean Algebras.Bohuslav Balcar, Thomas Jech & Jindřich Zapletal - 1997 - Annals of Pure and Applied Logic 87 (3):187-208.

Add more citations

Similar books and articles


Added to PP index

Total views
204 ( #49,748 of 2,445,258 )

Recent downloads (6 months)
1 ( #457,173 of 2,445,258 )

How can I increase my downloads?


My notes