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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 on generalized strongly normal extensions from [Pillay, “Differential Galois theory I”, Illinois Journal of Mathematics, 42(4), 1998], using this to give a restatement of a conjecture on almost semiabelian δ-groups from [Bertrand and Pillay, “Galois theory, functional Lindemann–Weierstrass, and Manin maps”, Pacific Journal of Mathematics, 281(1), 2016].

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[2] Brouette Q. and Point F.. On Galois groups of strongly normal extensions, preprint, 2015, arXiv:1512.95998v1.
[3] Cassidy P. J. and Singer M. F.. Galois theory of parameterized differential equations and linear differential algebraic groups , Differential Equations and Quantum Groups (Bertrand D., Enriquez B., Mitschi C., Sabbah C., and Schaefke R., editors), IRMA Lectures in Mathematics and Theoretical Physics, vol. 9, EMS Publishing House, Zürich, Switzerland, 2006, pp. 113157.
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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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