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[This paper replaces an earlier version by O. Leon Sanchez, Galois correspondence for differential Galois extensions, pdf]

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the constants are not “closed” in suitable senses. We also improve the definitions and results from [15] on generalized strongly normal extensions, using this to give a restatement of a conjecture from [1].

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Full text arXiv 1511.05541: pdf, ps.