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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 NY 10016, USA E-mail: gunter.fuchs@csi.cuny.edu URL: 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 ω 2, 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

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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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