The elementary theory of Dedekind cuts in polynomially bounded structures

Details The elementary theory of Dedekind cuts in polynomially bounded structures The elementary theory of Dedekind cuts in polynomially bounded structures

2003-05-08

arxiv.org/abs/math/0305122v2

Mathematics

Logic

16 pages. The paper is a sequel to http://www-nw.uni-regensburg.de/~.trm22116.mathematik.uni-regensburg.de/paper s/cutsa.ps

Scientific paper

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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