Extension of standard models of ZFC to models of Nelson's nonstandard set theory IST (Q1972520)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Extension of standard models of ZFC to models of Nelson's nonstandard set theory IST |
scientific article; zbMATH DE number 1429627
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extension of standard models of ZFC to models of Nelson's nonstandard set theory IST |
scientific article; zbMATH DE number 1429627 |
Statements
Extension of standard models of ZFC to models of Nelson's nonstandard set theory IST (English)
0 references
2 August 2000
0 references
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}.
0 references
Zermelo-Fraenkel set theory
0 references
internal set theory
0 references
axiomatic systems
0 references
ultrafilters
0 references
0 references
