Journal of Symbolic Logic

Heirs of box types in polynomially bounded structures

Marcus Tressl

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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 Mk, 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.

Article information

J. Symbolic Logic, Volume 74, Issue 4 (2009), 1225-1263.

First available in Project Euclid: 5 October 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: Primary 03C64 Secondary 13J30

model theory o-minimality real closed fields heirs weakly o-minimal model completeness Dedekind cuts valuation theory


Tressl, Marcus. Heirs of box types in polynomially bounded structures. J. Symbolic Logic 74 (2009), no. 4, 1225--1263. doi:10.2178/jsl/1254748689.

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