Strongly uplifting cardinals and the boldface resurrection axioms

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Archive for Mathematical Logic 56 (7-8):1115-1133 (2017)
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Abstract

We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost-hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.

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10.1007/s00153-017-0542-y

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Joel David Hamkins
Oxford University

Citations of this work

Diagonal reflections on squares.Gunter Fuchs - 2019 - Archive for Mathematical Logic 58 (1-2):1-26.
Hierarchies of resurrection axioms.Gunter Fuchs - 2018 - Journal of Symbolic Logic 83 (1):283-325.
Combining resurrection and maximality.Kaethe Minden - 2021 - Journal of Symbolic Logic 86 (1):397-414.

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References found in this work

The lottery preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
What is the theory without power set?Victoria Gitman, Joel David Hamkins & Thomas A. Johnstone - 2016 - Mathematical Logic Quarterly 62 (4-5):391-406.
Resurrection axioms and uplifting cardinals.Joel David Hamkins & Thomas A. Johnstone - 2014 - Archive for Mathematical Logic 53 (3-4):463-485.
The bounded proper forcing axiom.Martin Goldstern & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (1):58-73.
Strongly unfoldable cardinals made indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.

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