First-order undefinability of the notion of transfinitely uplifting cardinals

Research output: Contribution to journalArticle (Academic Journal)peer-review


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.
Original languageEnglish
Pages (from-to)105-115
Number of pages11
JournalMathematical Logic Quarterly
Issue number1
Early online date3 Apr 2021
Publication statusPublished - 14 Jun 2021

Bibliographical note

Funding Information:
I am most grateful to the anonymous referee for their meticulous feedback and helpful and constructive suggestions: in particular, the notion of a fully reflecting ordinal (and its naming) and the use of it to improve the presentation of my proofs are suggested by them. I would also like to thank Kentaro Sato and Philip Welch for fruitful discussions on some topics related to this?article.

Publisher Copyright:
© 2021 Wiley-VCH GmbH


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