Differential-algebraic jet spaces preserve internality to the constants

Zoe Chatzidakis; Matthew Harrison-Trainor; Rahim Moosa

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arXiv · 1311.3546

Differential-algebraic jet spaces preserve internality to the constants

Zoe Chatzidakis·Matthew Harrison-Trainor·Rahim Moosa

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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.

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BibTeX RIS

Zoe Chatzidakis, Matthew Harrison-Trainor, Rahim Moosa. 2013-11-14. Differential-algebraic jet spaces preserve internality to the constants. https://arxiv.org/abs/1311.3546

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