Differential-algebraic jet spaces preserve internality to the constants

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.