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STRONG DENSITY OF DEFINABLE TYPES AND CLOSED ORDERED DIFFERENTIAL FIELDS

Published online by Cambridge University Press:  30 January 2019

QUENTIN BROUETTE ,
PABLO CUBIDES KOVACSICS  and
FRANÇOISE POINT
QUENTIN BROUETTE
Affiliation:
DÉPARTEMENT DE MATHÉMATIQUE (DE VINCI) UNIVERSITÉ DE MONS 20 PLACE DU PARC B-7000 MONS, BELGIUM E-mail: quentin.brouette@umons.ac.be
PABLO CUBIDES KOVACSICS
Affiliation:
LABORATOIRE DE MATHÉMATIQUES NICOLAS ORESME UNIVERSITÉ DE CAEN CNRS UMR6139UNIVERSITÉ DE CAEN BP 5186 14032 CAEN CEDEX, FRANCE E-mail: pablo.cubides@unicaen.fr
FRANÇOISE POINT
Affiliation:
DÉPARTEMENT DE MATHÉMATIQUE (DE VINCI) UNIVERSITÉ DE MONS 20 PLACE DU PARC B-7000 MONS, BELGIUM E-mail: point@math.univ-paris-diderot.fr
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Abstract

The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable set X ⊆ Mn, there is a definable type p in X, definable over a code for X and of the same d-dimension as X. Both o-minimal theories and the theory of closed ordered differential fields (CODF) are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

Keywords

03C6412H0512L1203C45ordered differential fieldsdensity of definable typesclosed ordered differential fields
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 1099 - 1117
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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