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Strongly uplifting cardinals and the boldface resurrection axioms

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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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Authors and Affiliations

  1. Department of Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Joel David Hamkins

  2. Department of Philosophy, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Joel David Hamkins

  3. Department of Computer Science, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Joel David Hamkins

  4. Department of Mathematics, College of Staten Island of CUNY, Staten Island, NY, 10314, USA

    Joel David Hamkins

  5. Department of Mathematics, New York City College of Technology of CUNY, Brooklyn, NY, 11201, USA

    Thomas A. Johnstone

Authors
  1. Joel David Hamkins
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  2. Thomas A. Johnstone
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Correspondence to Joel David Hamkins.

Additional information

This article is a successor to [9]. The research of the first author has been supported in part by NSF Grant DMS-0800762, PSC-CUNY Grant 64732-00-42 and Simons Foundation Grant 209252, and the authors together are supported by Grant 80209-06 20 from the CUNY Collaborative Incentive Award program. The research of the second author has been supported by a CUNY Scholar Incentive Award, PSC-CUNY Grants 62803-00-40 and 64682-00-42, and by Grants P20835-N13 and P21968-N13 from the Austrian Science Fund (FWF) during his 2009–2010 visit to the Kurt Gödel Research Center at the University of Vienna. Commentary concerning this article can be made at http://jdh.hamkins.org/strongly-uplifting-cardinals-and-boldface-resurrection.

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Hamkins, J.D., Johnstone, T.A. Strongly uplifting cardinals and the boldface resurrection axioms. Arch. Math. Logic 56, 1115–1133 (2017). https://doi.org/10.1007/s00153-017-0542-y

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  • DOI: https://doi.org/10.1007/s00153-017-0542-y

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