On differential Galois groups of strongly normal extensions. (English) Zbl 1521.03086
Summary: We revisit E. R. Kolchin’s [Differential algebra and algebraic groups. New York, NY: Academic Press (1973; Zbl 0264.12102)] results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or \(p\)-valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in CODF, we establish a relative Galois correspondence for relatively definable subgroups of the group of differential order automorphisms.
Citations:
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