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Archive for Mathematical Logic

, Volume 56, Issue 7–8, pp 1115–1133 | Cite as

Strongly uplifting cardinals and the boldface resurrection axioms

  • Joel David Hamkins
  • Thomas A. Johnstone
Article

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.

Keywords

Large cardinals Forcing Resurrection axiom 

Mathematics Subject Classification

03E55 03E57 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe Graduate Center of the City University of New YorkNew YorkUSA
  2. 2.Department of PhilosophyThe Graduate Center of the City University of New YorkNew YorkUSA
  3. 3.Department of Computer ScienceThe Graduate Center of the City University of New YorkNew YorkUSA
  4. 4.Department of MathematicsCollege of Staten Island of CUNYStaten IslandUSA
  5. 5.Department of MathematicsNew York City College of Technology of CUNYBrooklynUSA

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