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 (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	Pure Connector
Date Deposited:	01 Nov 2013 14:08
Last Modified:	28 Mar 2025 05:22
URI:	https://ueaeprints.uea.ac.uk/id/eprint/44044
DOI:	10.1016/S0168-0072(00)00058-0

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