MODEL COMPLETENESS OF O-MINIMAL FIELDS WITH CONVEX VALUATIONS
نویسندگان
چکیده
منابع مشابه
Model Completeness of O-Minimal Fields with Convex Valuations
We let R be an o-minimal expansion of a field, V a convex subring, and (R0, V0) 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 LR0 be the language L expanded by constants for all elements of R0. Our main result is that (R, V ) considered as an LR0-structure is model com...
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Let R be an o-minimal field with a proper convex subring V . We axiomatize the class of all structures (R, V ) such that kind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in [8] it was shown that certain first order conditions on (R, V ) are sufficient for the o-minimality of kind. Here we prove that these conditions are also ...
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Contents 1. Introduction. 2. Heirs. 3. The invariance group of a cut. 4. Review of T-convex valuation rings. 5. The invariance valuation ring of a cut. 6. A method for producing cuts with prescribed signature. 7. Existentially closed extensions. 1. Introduction. Let M be a totally ordered set. A (Dedekind) cut p of M is a couple (p L , p R) of subsets p L , p R of M such that p L ∪ p R = M and ...
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In their paper [D–M–M2], van den Dries, Macintyre and Marker give an explicit construction of a nonarchimedean model of the theory of the reals with restricted analytic functions and exponentiation. This model, called the logarithmic exponential power series field, lies in a generalized power series field. They use the results of Ressayre and Mourgues about truncation-closed embeddings to answe...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2015
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2014.3