Real Algebraic and Analytic Geometry
Submission: 2009, January 6.
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 Mk, definable in the expansion M* of M by all convex subsets of the line. Moreover we show that M* is model complete after naming constants.
Mathematics Subject Classification (2000): 03C64, 13J30.
Keywords and Phrases: model theory, o-minimality, real closed fields, heirs, weakly o-minimal, model completeness.
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