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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An equivalent form of Lévy's axiom schema


Author: Murray Jorgensen
Journal: Proc. Amer. Math. Soc. 26 (1970), 651-654
MSC: Primary 02.68
DOI: https://doi.org/10.1090/S0002-9939-1970-0269498-7
MathSciNet review: 0269498
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0269498-7
Keywords: Axiom schema, fixed point of normal function, inaccessible cardinals, transfinite number, ordinal
Article copyright: © Copyright 1970 American Mathematical Society