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The elementary theory of Dedekind cuts in polynomially bounded structures

Marcus Tressl
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Abstract

Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M, which yields a description of all subsets of M^n, definable in the expanded structure.

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Marcus Tressl. 2003-05-09. The elementary theory of Dedekind cuts in polynomially bounded structures. https://arxiv.org/abs/math/0305122

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