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HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES

Published online by Cambridge University Press:  01 May 2018

GUNTER FUCHS
GUNTER FUCHS*
Affiliation:
THE COLLEGE OF STATEN ISLAND (CUNY) 2800 VICTORY BLVD. STATEN ISLAND, NY 10314, USA and THE GRADUATE CENTER (CUNY) 365 5TH AVENUE, NEW YORK NY10016, USAE-mail:[email protected]: www.math.csi.cuny.edu/∼fuchs
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Abstract

I analyze the hierarchies of the bounded and the weak bounded forcing axioms, with a focus on their versions for the class of subcomplete forcings, in terms of implications and consistency strengths. For the weak hierarchy, I provide level-by-level equiconsistencies with an appropriate hierarchy of partially remarkable cardinals. I also show that the subcomplete forcing axiom implies Larson’s ordinal reflection principle at ω2, and that its effect on the failure of weak squares is very similar to that of Martin’s Maximum.

Keywords

03E0503E4003E5003E5503E57forcing axiomssubcomplete forcingsquare principlesremarkable cardinalsweak forcing axiomsbounded forcing axioms
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 256 - 282
Copyright
Copyright © The Association for Symbolic Logic 2018 

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