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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*
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

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2018 

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