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We let R be an o-minimal expansion of a field, V a convex subring, and (R 0 , V 0) an elementary substructure of (R, V). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate for V , and we let L R 0 be the language L expanded by constants for all elements of R 0. Our main result is that (R, V)… (More)

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