The structure of Dedekind cardinals

Ellentuck, Erik

doi:10.1090/S0002-9947-1973-0325396-9

The structure of Dedekind cardinals
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by Erik Ellentuck

Trans. Amer. Math. Soc. 180 (1973), 109-125

DOI: https://doi.org/10.1090/S0002-9947-1973-0325396-9

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Abstract:

Semantic criteria are given for provability in set theory without the axiom of choice of positive sentences about the Dedekind cardinals. These criteria suggest that Dedekind cardinals (as well as general cardinals) have an internal structure.

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Arithmetically isolated sets and nonstandard models

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