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On some algebraic questions of nonstandard analysis. (English. Russian original) Zbl 0616.03045

Sov. Math., Dokl. 31, 30-34 (1985); translation from Dokl. Akad. Nauk SSSR 280, 38-41 (1985).
The author takes as the basic idea of nonstandard analysis the notion that many ”complex” mathematical objects can be made to appear ”simple” with the proper choice of set-theoretic model. Certain properties of these simplified objects then become apparent; and, through transfer theorems, one shows that related properties hold for the original complex objects.
In the present paper the results are quite technical. Suffice it to say that the models of interest are the Heyting-valued models (with truth values in a Heyting algebra), the mathematical objects to be studied are rings and modules, and the properties in question are first-order properties expressible via Horn formulas.
Reviewer: P.Bankston

MSC:

03H99 Nonstandard models
03C62 Models of arithmetic and set theory
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