On hereditarily countable sets

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1982 English Publisher:Cambridge University Press (CUP)Journal:Journal of Symbolic Logic, volume 47, pages 43-47 (issn: 0022-4812, eissn: 1943-5886,

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Authors: Thomas Jech;

doi: 10.2307/2273380

On hereditarily countable sets

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Abstract

AbstractIt is shown (in ZF) that every hereditarily countable set has rank less than ω2, and that if ℵ1 is singular then there are hereditarily countable sets of all ranks less than ω2.

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Pennsylvania State University
United States

Keywords

Large cardinals, hereditarily countable sets, Ordinal and cardinal numbers, axiom of choice, Axiom of choice and related propositions, Consistency and independence results

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