This paper is devoted to an extension of Kolchin's Galois theory of differential fields. When we say an "extension" of Kolchin's theory, we mean that a larger class of differential field extensions F < K is subsumed by our theory. Kolchin's theory was itself an extension, in the context of differential algebra, of the classical Picard-Vessiot theory. Kolchin called his differential field extensions strongly normal. In the Picard-Vessiot theory, the Galois groups have a natural structure as algebraic matrix groups over the constants (namely algebraic subgroups of GL(n, C)), where C denotes the constants of the differential field F).
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