Heirs of box types in polynomially bounded structures

Marcus Tressl

doi:10.2178/jsl/1254748689

Heirs of box types in polynomially bounded structures

Research output: Contribution to journal › Article › peer-review

Abstract

A box type is an n-rype 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.

Original language	English
Pages (from-to)	1225-1263
Number of pages	39
Journal	The Journal of Symbolic Logic
Volume	74
Issue number	4
DOIs	https://doi.org/10.2178/jsl/1254748689
Publication status	Published - 1 Dec 2009

Keywords

Dedekind cuts
Heirs
Model completeness
Model theory
O-minimality
Real closed fields
Valuation theory
Weakly o-minimal

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abstract = "A box type is an n-rype 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.",

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AB - A box type is an n-rype 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.

KW - Dedekind cuts

KW - Heirs

KW - Model completeness

KW - Model theory

KW - O-minimality

KW - Real closed fields

KW - Valuation theory

KW - Weakly o-minimal

U2 - 10.2178/jsl/1254748689

DO - 10.2178/jsl/1254748689

M3 - Article

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VL - 74

SP - 1225

EP - 1263

JO - The Journal of Symbolic Logic

JF - The Journal of Symbolic Logic

IS - 4

ER -

Heirs of box types in polynomially bounded structures

Abstract

Keywords

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