Journal of Symbolic Logic

An axiomatic presentation of the nonstandard methods in mathematics

Mauro Di Nasso

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Abstract

A nonstandard set theory ∗ZFC is proposed that axiomatizes the nonstandard embedding ∗. Besides the usual principles of nonstandard analysis, all axioms of ZFC except regularity are assumed. A strong form of saturation is also postulated. ∗ZFC is a conservative extension of ZFC.

Article information

Source
J. Symbolic Logic, Volume 67, Issue 1 (2002), 315-325.

Dates
First available in Project Euclid: 18 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1190150046

Digital Object Identifier
doi:10.2178/jsl/1190150046

Mathematical Reviews number (MathSciNet)
MR1889553

Zentralblatt MATH identifier
1005.03053

Subjects
Primary: 03E70: Nonclassical and second-order set theories
Secondary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]

Citation

Di Nasso, Mauro. An axiomatic presentation of the nonstandard methods in mathematics. J. Symbolic Logic 67 (2002), no. 1, 315--325. doi:10.2178/jsl/1190150046. https://projecteuclid.org/euclid.jsl/1190150046


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