Differential-algebraic jet spaces preserve internality to the constants

摘要

This paper concerns the model theory of jet spaces (i.e., higher-ordertangent spaces) in differentially closed fields. Suppose p is the generic typeof the jet space to a finite dimensional differential-algebraic variety at ageneric point. It is shown that p satisfies a certain strengthening of almostinternality to the constant field called "preserving internality to theconstants". This strengthening is a model-theoretic abstraction of the genericbehaviour of jet spaces in complex-analytic geometry. A counterexample isconstructed showing that only this generic analogue holds indifferential-algebraic geometry.