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HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS

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, USA E-mail:[email protected]: www.math.csi.cuny.edu/∼fuchs
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Abstract

I analyze the hierarchies of the bounded resurrection axioms and their “virtual” versions, the virtual bounded resurrection axioms, for several classes of forcings (the emphasis being on the subcomplete forcings). I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for subcomplete or countably closed forcing imply the failure of Todorčević’s square at the appropriate level. I also establish connections between these hierarchies and the hierarchies of bounded and weak bounded forcing axioms.

Keywords

03E0503E4003E5003E5503E57forcing axiomsresurrection axiomssubcomplete forcingsquare principlesremarkable cardinalsextendible cardinalsvirtually extendible cardinalsweak forcing axiomsbounded forcing axioms
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 283 - 325
Copyright
Copyright © The Association for Symbolic Logic 2018 

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