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Second-Order Characterizable Cardinals and Ordinals

Benjamin R. George
Studia Logica: An International Journal for Symbolic Logic
Vol. 84, No. 3 (Dec., 2006), pp. 425-449
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016843
Page Count: 25
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Second-Order Characterizable Cardinals and Ordinals
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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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