Second-order characterizable cardinals and ordinals

Studia Logica 84 (3):425 - 449 (2006)
The notions of finite and infinite second-order characterizability of cardinal and ordinal numbers are developed. Several known results for the case of finite characterizability are extended to infinite characterizability, and investigations of the second-order theory of ordinals lead to some observations about the Fraenkel-Carnap question for well-orders and about the relationship between ordinal characterizability and ordinal arithmetic. The broader significance of cardinal characterizability and the relationships between different notions of characterizability are also discussed.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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Azriel Levy (1981). Basic Set Theory. Philosophical Review 90 (2):298-300.
G. Au George Weaver (2005). Fraenkel-Carnap Properties. Mathematical Logic Quarterly 51 (3):285.

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