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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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  1. Department of Linguistics, UCLA, 3125 Campbell Hall, Box 951543, Los Angeles, California, USA, 90095-1543

    Benjamin R. George

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  1. Benjamin R. George
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Correspondence to Benjamin R. George.

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AMS subject classification : 03B15 and 03C85

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George, B.R. Second-Order Characterizable Cardinals and Ordinals. Stud Logica 84, 425–449 (2006). https://doi.org/10.1007/s11225-006-9016-7

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  • DOI: https://doi.org/10.1007/s11225-006-9016-7

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