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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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 |
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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: | 24 Oct 2022 04:54 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/44044 |
DOI: | 10.1016/S0168-0072(00)00058-0 |
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