Translator Disclaimer
March 2008 The number of openly generated Boolean algebras
Stefan Geschke, Saharon Shelah
J. Symbolic Logic 73(1): 151-164 (March 2008). DOI: 10.2178/jsl/1208358746

Abstract

This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly σ-filtered Boolean algebras. We show that for every uncountable regular cardinal κ there are 2κ pairwise non-isomorphic openly generated Boolean algebras of size κ≥ℵ1 provided there is an almost free non-free abelian group of size κ. The openly generated Boolean algebras constructed here are almost free. Moreover, for every infinite regular cardinal κ we construct 2κ pairwise non-isomorphic Boolean algebras of size κ that are tightly σ-filtered and c.c.c. These two results contrast nicely with Koppelberg’s theorem in [12] that for every uncountable regular cardinal κ there are only 2 isomorphism types of projective Boolean algebras of size κ.

Citation

Download Citation

Stefan Geschke. Saharon Shelah. "The number of openly generated Boolean algebras." J. Symbolic Logic 73 (1) 151 - 164, March 2008. https://doi.org/10.2178/jsl/1208358746

Information

Published: March 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1137.06006
MathSciNet: MR2387936
Digital Object Identifier: 10.2178/jsl/1208358746

Subjects:
Primary: 06E05

Rights: Copyright © 2008 Association for Symbolic Logic

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.73 • No. 1 • March 2008
Back to Top