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 | References | Similar Articles | Additional Information
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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M. Jorgensen, An equivalent form of Lévy’s axiom schema, Notices Amer. Math. Soc. 16 (1969), 1086-1087. Abstract #69T-E82.
- Azriel Lévy, Axiom schemata of strong infinity in axiomatic set theory, Pacific J. Math. 10 (1960), 223–238. MR 124205
- Richard Montague, Two contributions to the foundations of set theory, Logic, Methodology and Philosophy of Science (Proc. 1960 Internat. Congr.), Stanford Univ. Press, Stanford, Calif., 1962, pp. 94–110. MR 0154804 A. Tarski, Über unerreichbare Kardinalzahlen, Fund. Math. 30 (1938), 68-89.
- Oswald Veblen, Continuous increasing functions of finite and transfinite ordinals, Trans. Amer. Math. Soc. 9 (1908), no. 3, 280–292. MR 1500814, DOI https://doi.org/10.1090/S0002-9947-1908-1500814-9
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Additional Information
Keywords:
Axiom schema,
fixed point of normal function,
inaccessible cardinals,
transfinite number,
ordinal
Article copyright:
© Copyright 1970
American Mathematical Society