Resurrection axioms and uplifting cardinals
Joel David Hamkins, Thomas A. Johnstone
TL;DR
This paper introduces resurrection axioms and uplifting cardinals, establishing their equiconsistency over ZFC and exploring their foundational implications in set theory.
Contribution
It presents new classes of forcing axioms and large cardinal notions, linking them through equiconsistency results.
Findings
Resurrection axioms are consistent with ZFC assuming uplifting cardinals.
Various instances of resurrection axioms are shown to be equiconsistent with uplifting cardinals.
The paper develops the theory connecting forcing axioms with large cardinal hypotheses.
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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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Homotopy and Cohomology in Algebraic Topology