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DIFFERENTIAL-ALGEBRAIC JET SPACES PRESERVE INTERNALITY TO THE CONSTANTS

Published online by Cambridge University Press:  22 July 2015

ZOE CHATZIDAKIS ,
MATTHEW HARRISON-TRAINOR  and
RAHIM MOOSA
ZOE CHATZIDAKIS
Affiliation:
DÉPARTEMENT DE MATHÉMATIQUES ET APPLICATIONS (UMR 8553) ECOLE NORMALE SUPÉRIEURE 45 RUE D’ULM, 75230 PARIS CEDEX 5FRANCEE-mail: zoe.chatzidakis@ens.fr
MATTHEW HARRISON-TRAINOR
Affiliation:
UNIVERSITY OF CALIFORNIA BERKELEY, DEPARTMENT OF MATHEMATICS 970 EVANS HALL, BERKELEY, CA 94720-3840, USAE-mail: mattht@math.berkeley.edu
RAHIM MOOSA
Affiliation:
UNIVERSITY OF WATERLOO DEPARTMENT OF PURE MATHEMATICS 200 UNIVERSITY AVENUE WEST WATERLOO, ONTARIO N2L 3G1 CANADAE-mail: rmoosa@uwaterloo.ca
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Abstract

Suppose p is the generic type of a differential-algebraic jet space to a finite dimensional differential-algebraic variety at a generic point. It is shown that p satisfies a certain strengthening of almost internality to the constants. This strengthening, which was originally called “being Moishezon to the constants” in [9] but is here renamed preserving internality to the constants, is a model-theoretic abstraction of the generic behaviour of jet spaces in complex-analytic geometry. An example is given showing that only a generic analogue holds in the differential-algebraic case: there is a finite dimensional differential-algebraic variety X with a subvariety Z that is internal to the constants, such that the restriction of the differential-algebraic tangent bundle of X to Z is not almost internal to the constants.

Keywords

differentially closed fieldsfinite rank definable setsinternality to the constantsKolchin’s differential tangent space
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 3 , September 2015 , pp. 1022 - 1034
Copyright
Copyright © The Association for Symbolic Logic 2015 

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