Ultraproducts and Ultra-Limits of Near-Rings.
P. Fuchs, G. Pilz (1985)
Monatshefte für Mathematik
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P. Fuchs, G. Pilz (1985)
Monatshefte für Mathematik
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A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed...
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