The number of openly generated Boolean algebras

Journal of Symbolic Logic 73 (1):151-164 (2008)
Abstract
This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly ϭ-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 > N1 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 ϭ-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<κ isomorphism types of projective Boolean algebras of size κ
Keywords Projective Boolean algebra   openly generated   almost free   tightly σ-filtered
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Yde Venema (2003). Atomless Varieties. Journal of Symbolic Logic 68 (2):607-614.
    Analytics

    Monthly downloads

    Sorry, there are not enough data points to plot this chart.

    Added to index

    2010-09-12

    Total downloads

    0

    Recent downloads (6 months)

    0

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.