Definable types in the theory of closed ordered differential fields

Brouette, Quentin

doi:10.1007/s00153-016-0517-4

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…Motivated (in part) by the fact that in CODF, isolated types are not dense, the first author had shown in his thesis that definable types are dense (see [Bro15] and [Bro17]). A key difference with the present work is that we carefully take into account the parameters over which types are defined.…”

Section: Introductionmentioning

confidence: 99%

Strong Density of Definable Types and Closed Ordered Differential Fields

Brouette¹,

Kovacsics²,

Point³

2019

J. symb. log.

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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 ⊆ M n , 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.

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Section: Introductionmentioning

confidence: 99%

Strong Density of Definable Types and Closed Ordered Differential Fields

Brouette¹,

Kovacsics²,

Point³

2019

J. symb. log.

Self Cite

View full text Add to dashboard Cite

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Definability of types and VC density in differential topological fields

Point

2017

Arch. Math. Logic

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Pro-definability of spaces of definable types

Kovacsics

2021

Proc. Amer. Math. Soc. Ser. B

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We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, p p -adically closed fields, real closed and algebraically closed valued fields and closed ordered differential fields. Furthermore, we prove pro-definability of other distinguished subspaces, some of which have an interesting geometric interpretation. Our general strategy consists of showing that definable types are uniformly definable, a property which implies pro-definability using an argument due to E. Hrushovski and F. Loeser. Uniform definability of definable types is finally achieved by studying classes of stably embedded pairs.

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Definable types in the theory of closed ordered differential fields

Cited by 3 publications

References 6 publications

Strong Density of Definable Types and Closed Ordered Differential Fields

Strong Density of Definable Types and Closed Ordered Differential Fields

Definability of types and VC density in differential topological fields

Pro-definability of spaces of definable types

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