A maximal bounded forcing axiom

Journal of Symbolic Logic 67 (1):130-142 (2002)
After presenting a general setting in which to look at forcing axioms, we give a hierarchy of generalized bounded forcing axioms that correspond level by level, in consistency strength, with the members of a natural hierarchy of large cardinals below a Mahlo. We give a general construction of models of generalized bounded forcing axioms. Then we consider the bounded forcing axiom for a class of partially ordered sets Γ 1 such that, letting Γ 0 be the class of all stationary-set-preserving partially ordered sets, one can prove the following: (a) $\Gamma_0 \subseteq \Gamma_1$ , (b) Γ 0 = Γ 1 if and only if NS ω 1 is ℵ 1 -dense. (c) If P $\notin \Gamma_1$ , then BFA({P}) fails. We call the bounded forcing axiom for Γ 1 Maximal Bounded Forcing Axiom (MBFA). Finally we prove MBFA consistent relative to the consistency of an inaccessible Σ 2 -correct cardinal which is a limit of strongly compact cardinals
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 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.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    Thilo Weinert (2010). The Bounded Axiom A Forcing Axiom. Mathematical Logic Quarterly 56 (6):659-665.
    Similar books and articles

    Monthly downloads

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

    Added to index


    Total downloads

    1 ( #306,128 of 1,088,426 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,426 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

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