An axiomatic presentation of the nonstandard methods in mathematics

Journal of Symbolic Logic 67 (1):315-325 (2002)
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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.

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