Second-Order Characterizable Cardinals and Ordinals

Studia Logica 84 (3):425-449 (2006)
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Abstract

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.

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2007

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10.1007/s11225-006-9016-7

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Ben George
University of Arizona

Citations of this work

Fraenkel–Carnap Questions for Equivalence Relations.George Weaver & Irena Penev - 2011 - Australasian Journal of Logic 10:52-66.

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References found in this work

Basic Set Theory.William Mitchell - 1981 - Journal of Symbolic Logic 46 (2):417-419.

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