Resurrection axioms and uplifting cardinals

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Archive for Mathematical Logic 53 (3-4):463-485 (2014)
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Abstract

We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances of the resurrection axioms are equiconsistent over ZFC with the existence of an uplifting cardinal.

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10.1007/s00153-014-0374-y

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Joel David Hamkins
Oxford University

Citations of this work

Virtual large cardinals.Victoria Gitman & Ralf Schindler - 2018 - Annals of Pure and Applied Logic 169 (12):1317-1334.
Martin’s maximum revisited.Matteo Viale - 2016 - Archive for Mathematical Logic 55 (1-2):295-317.
Diagonal reflections on squares.Gunter Fuchs - 2019 - Archive for Mathematical Logic 58 (1-2):1-26.

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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.
Bounded forcing axioms as principles of generic absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.
Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
A simple maximality principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
The bounded proper forcing axiom.Martin Goldstern & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (1):58-73.

View all 15 references / Add more references