Hierarchies of resurrection axioms

Journal of Symbolic Logic 83 (1):283-325 (2018)
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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. 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.

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Citations of this work

Subcomplete forcing principles and definable well‐orders.Gunter Fuchs - 2018 - Mathematical Logic Quarterly 64 (6):487-504.

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References found in this work

Bounded forcing axioms as principles of generic absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Resurrection axioms and uplifting cardinals.Joel David Hamkins & Thomas A. Johnstone - 2014 - Archive for Mathematical Logic 53 (3-4):463-485.
Simultaneous stationary reflection and square sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.

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