First-order undefinability of the notion of transfinitely uplifting cardinals

Kentaro Fujimoto

doi:10.1002/malq.201800050

First-order undefinability of the notion of transfinitely uplifting cardinals

Kentaro Fujimoto

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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.

Original language	English
Pages (from-to)	105-115
Number of pages	11
Journal	Mathematical Logic Quarterly
Volume	67
Issue number	1
Early online date	3 Apr 2021
DOIs	https://doi.org/10.1002/malq.201800050
Publication status	Published - 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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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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First-order undefinability of the notion of transfinitely uplifting cardinals

Abstract

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