A NOTE ON CANONICAL BASES IN PARTIAL DIFFERENTIAL

This note is intended as a supplement for the slides I gave at a November 2012 Kolchin seminar talk. I rework some of the definitions and explain some of the model-theoretic notation in differential algebraic terms. 1. Bounding the Kolchin polynomial of a relative canonical base In this section, we will discuss tuples which generate differential fields over which a given type does not fork (what might be called a relative canonical base or a relative field of definition). Versions of this lemma appeared in preprints of my paper about indecomposability. Thanks very much to P. Cassidy and W. Sit for numerous discussions of the result. Following suggestions by the members of the Kolchin seminar, I have reworked some of the definitions and proofs of the result in order to make them more accessible to non-model theorists; this theorem is equiva-lent to the one which can be found in a copy of my thesis at my Berkeley webpag