Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST
Copyright policy )Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST
The authors characterize the standard models of \textbf{ZFC} set theory that can be embedded as a class of standard sets in models of internal set theory, \textbf{IST}. The basic problem is to describe the transitive \(\in\)-models of \textbf{ZFC} that can be extended to a model of \textbf{IST}. The authors derive sufficient conditions for the existence of such an extension, which are necessary for the \textbf{IST}\(^+\) theory that is obtained by adding a certain natural form of the axiom of choice to \textbf{IST}.
- Lomonosov Moscow State University Russian Federation
- University of Wuppertal Germany
Models of arithmetic and set theory, internal set theory, Zermelo-Fraenkel set theory, axiomatic systems, Nonstandard models in mathematics, Nonclassical and second-order set theories, ultrafilters
Models of arithmetic and set theory, internal set theory, Zermelo-Fraenkel set theory, axiomatic systems, Nonstandard models in mathematics, Nonclassical and second-order set theories, ultrafilters
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