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1 results

  • DIFFERENTIAL-ALGEBRAIC JET SPACES PRESERVE INTERNALITY TO THE CONSTANTS

  • ZOE CHATZIDAKIS, MATTHEW HARRISON-TRAINOR, RAHIM MOOSA
  • Journal:
    The Journal of Symbolic Logic / Volume 80 / Issue 3 / September 2015
    Published online by Cambridge University Press:
    22 July 2015, pp. 1022-1034
    Print publication:
    September 2015

  • 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.