An Axiomatic Presentation of the Nonstandard Methods in Mathematics

Journal of Symbolic Logic 67 (1):315 - 325 (2002)
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.
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DOI 10.2178/jsl/1190150046
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Peter Fletcher (1989). Nonstandard Set Theory. Journal of Symbolic Logic 54 (3):1000-1008.

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