A maximal bounded forcing axiom

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

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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
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	Pure Connector
Date Deposited:	01 Nov 2013 14:06
Last Modified:	11 Sep 2023 15:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/44045
DOI:	10.2178/jsl/1190150034

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