On the existence of factor sets by external equivalences in IST. (Russian, English) Zbl 1017.03041

Sib. Mat. Zh. 43, No. 4, 879-886 (2002); translation in Sib. Math. J. 43, No. 4, 708-713 (2002).
From the author’s abstract: In the framework of the theory IST of nonstandard analysis, the possibility to define factor sets of the real line modulo external equivalence relations by means of external formulas is studied. The case of additive convex equivalence whose equivalence classes are defined by a formula with external universal quantifiers is considered. It is shown that in this case there exists an external function selecting one representative from each equivalence class if and only if the relation in question coincides up to translation and dilation with the relation of infinite proximity.


03H05 Nonstandard models in mathematics
03E70 Nonclassical and second-order set theories
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