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Preprint Number 657

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657. Zoé Chatzidakis, Matthew Harrison-Trainor, Rahim Moosa
Differential-algebraic jet spaces preserve internality to the constants
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Submission date: 14 November 2013

Abstract:

This paper concerns the model theory of jet spaces (i.e., higher-order tangent spaces) in differentially closed fields. Suppose p is the generic type of the 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 constant field called “preserving internality to the constants”. This strengthening is a model-theoretic abstraction of the generic behaviour of jet spaces in complex-analytic geometry. A counterexample is constructed showing that only this generic analogue holds in differential-algebraic geometry.

Mathematics Subject Classification: 03C45, 12H05

Keywords and phrases:

Full text arXiv 1311.3546: pdf, ps.


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