Bounded forcing axioms and the continuum

Asperó, David and Bagaria, Joan (2001) Bounded forcing axioms and the continuum. Annals of Pure and Applied Logic, 109 (3). pp. 179-203. ISSN 0168-0072

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Abstract

We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (?,?)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the level ?, and therefore with the existence of an ?-Suslin tree. We also show that the axiom we call BMM implies ?=?, as well as a stationary reflection principle which has many of the consequences of Martin's Maximum for objects of size ?. Finally, we give an example of a so-called boldface bounded forcing axiom implying 2=?.

Item Type: Article
Uncontrolled Keywords: bounded forcing axioms,gaps,open coloring axiom,the continuum,boldface bounded forcing axioms
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Pure Connector
Date Deposited: 01 Nov 2013 14:08
Last Modified: 11 Oct 2019 10:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/44044
DOI: 10.1016/S0168-0072(00)00058-0

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