Journal of Symbolic Logic 74 (4):1225 - 1263 (2009)

Abstract
A box type is an n-type of an o-minimal structure which is uniquely determined by the projections to the coordinate axes. We characterize heirs of box types of a polynomially bounded o-minimal structure M. 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. We show that M after naming constants, is model complete provided M is model complete
Keywords model theory   o-minimality   real closed fields   heirs   weakly o-minimal   model completeness   Dedekind cuts   valuation theory
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DOI 10.2178/jsl/1254748689
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References found in this work BETA

[Omnibus Review].Anand Pillay - 1984 - Journal of Symbolic Logic 49 (1):317-321.
Forking and Independence in o-Minimal Theories.Alfred Dolich - 2004 - Journal of Symbolic Logic 69 (1):215-240.
Weakly o-Minimal Nonvaluational Structures.Roman Wencel - 2008 - Annals of Pure and Applied Logic 154 (3):139-162.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.

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