Submission date:11 August 2006

Abstract:

We characterize heirs of so called box types of a polynomially bounded o-minimal structure M. A box type is an n-type of M which is uniquely determined by the projections to the coordinate axes. From this, we deduce various structure theorems for subsets of M^k, definable in the expansion M^* of M by all convex subsets of the line. Moreover we obtain a model completeness result for M^*.

Mathematics Subject Classification: 03C64; Secondary 13J30

Keywords and phrases: model theory, o-minimality, real closed fields, heirs, weakly o-minimal, model completeness.

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