On differential Galois groups of strongly normal extensions

Mathematical Logic Quarterly 64 (3):155-169 (2018)
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Abstract

We revisit Kolchin's 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, we establish a relative Galois correspondence for relatively definable subgroups of the group of differential order automorphisms.

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First order topological structures and theories.Anand Pillay - 1987 - Journal of Symbolic Logic 52 (3):763-778.
Topological differential fields.Nicolas Guzy & Françoise Point - 2010 - Annals of Pure and Applied Logic 161 (4):570-598.
Superstable differential fields.A. Pillay & Ž Sokolović - 1992 - Journal of Symbolic Logic 57 (1):97-108.
Some definable galois theory and examples.Omar León Sánchez & Anand Pillay - 2017 - Bulletin of Symbolic Logic 23 (2):145-159.

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