## A characterization of internal sets.(English)Zbl 0686.03039

The paper deals with a universe of sets satisfying the usual axioms of Zermelo-Fraenkel set theory with atoms (urelements). It is assumed that $${\mathbb{R}}$$, the set of real numbers, is represented by a set of atoms. If in this universe of sets, A is the superstructure based on $${\mathbb{R}}$$, then the theory $${\mathcal A}:=(A;\in | A^ 2;id| A^ 2)$$ is called “standard analysis”. The author considers nonstandard models of the theory of $${\mathcal A}$$ that are proper extensions of $${\mathcal A}$$. The main result of the paper is a characterization of the class of internal sets as the unique subclass of the model that contains the standard sets, is transitive and membership well-founded.
Reviewer: W.A.J.Luxemburg

### MSC:

 03H05 Nonstandard models in mathematics
Full Text:

### References:

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