First‐order undefinability of the notion of transfinitely uplifting cardinals

Mathematical Logic Quarterly 67 (1):105-115 (2021)
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Abstract

Audrito and Viale introduced the new large cardinal notion of an (α)‐uplifting cardinal (for an ordinal α). We shall show that this notion cannot be defined (or expressed) in the standard first‐order language of set theory for every tranfinite α.

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10.1002/malq.201800050

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Kentaro Fujimoto
University of Bristol

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Classes and truths in set theory.Kentaro Fujimoto - 2012 - Annals of Pure and Applied Logic 163 (11):1484-1523.
Resurrection axioms and uplifting cardinals.Joel David Hamkins & Thomas A. Johnstone - 2014 - Archive for Mathematical Logic 53 (3-4):463-485.
Absoluteness via resurrection.Giorgio Audrito & Matteo Viale - 2017 - Journal of Mathematical Logic 17 (2):1750005.

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