An axiomatic presentation of the nonstandard methods in mathematics
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.
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1190150046
Mathematical Reviews number (MathSciNet): MR1889553
Digital Object Identifier: doi:10.2178/jsl/1190150046
Zentralblatt MATH identifier: 1005.03053