Asperó, D.
(2002)
*A maximal bounded forcing axiom.*
Journal of Symbolic Logic, 67 (1).
pp. 130-142.
ISSN 0022-4812

## Abstract

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 G such that, letting G be the class of all stationary-set-preserving partially ordered sets, one can prove the following: (a) G ? G, (b) G = G if and only if NS is N-dense. (c) If P ? G, then BFA({P}) fails. We call the bounded forcing axiom for G Maximal Bounded Forcing Axiom (MBFA). Finally we prove MBFA consistent relative to the consistency of an inaccessible S-correct cardinal which is a limit of strongly compact cardinals.

Item Type: | Article |
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Faculty \ School: | Faculty of Science > School of Mathematics |

Related URLs: | |

Depositing User: | Pure Connector |

Date Deposited: | 01 Nov 2013 14:06 |

Last Modified: | 24 Oct 2022 04:54 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/44045 |

DOI: |

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