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Pairs of theories satisfying a Mordell-Lang condition. (English) Zbl 1461.03028

The present paper continues studying properties of pairs of structures (or theories). The authors obtain a characterization for decidability of the theory of an ordered \(K\)-vector space expanded by a predicate for \(\mathbb{Q}\), where \(K\) is a subfield of \(\mathbb{R}\). They also establish that there exists a non-real closed subfield \(K\) of a real closed field such that every open set definable in the expansion of the real field by \(K\) is semialgebraic.

MSC:

03C64 Model theory of ordered structures; o-minimality
03C10 Quantifier elimination, model completeness, and related topics
03B25 Decidability of theories and sets of sentences
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces

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References:

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