Baumgartner's conjecture and bounded forcing axioms

Asperó, David, Friedman, Sy-David, Mota, Miguel Angel and Sabok, Marcin (2013) Baumgartner's conjecture and bounded forcing axioms. Annals of Pure and Applied Logic, 164 (12). pp. 1178-1786. ISSN 0168-0072

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Abstract

We study the spectrum of forcing notions between the iterations of s-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of a-proper forcings for indecomposable countable ordinals a, the Axiom A forcings and forcings completely embeddable into an iteration of a s-closed followed by a ccc forcing. For the latter class, we present an equivalent characterization in terms of Baumgartner's Axiom A. This resolves a conjecture of Baumgartner from the 1980s. We also study the bounded forcing axioms for the hierarchy of a-proper forcings. Following ideas of Shelah we separate them for distinct countable indecomposable ordinals.

Item Type: Article
Uncontrolled Keywords: proper forcing,axiom a forcing,bounded forcing axioms
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Pure Connector
Date Deposited: 04 Nov 2013 22:09
Last Modified: 21 Apr 2020 22:07
URI: https://ueaeprints.uea.ac.uk/id/eprint/44209
DOI: 10.1016/j.apal.2013.06.006

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