An Equivalent Form of Levy's Axiom Schema

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 1970Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 26, page 651 (issn: 0002-9939,

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Authors: Jorgensen, Murray;

doi: 10.2307/2037129 , 10.1090/s0002-9939-1970-0269498-7

An Equivalent Form of Levy's Axiom Schema

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Abstract

A generalized notion of ordinal inaccessibility is defined. A characterization of this notion in terms of normal ordinal functions yields as a consequence that a schema analogous to a form of Tarski’s Axiom of Inaccessible Cardinals is equivalent to Lévy’s axiom schema under the axiom of choice.

Keywords

Ordinal and cardinal numbers

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