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SOME DEFINABLE GALOIS THEORY AND EXAMPLES

Published online by Cambridge University Press:  21 June 2017

OMAR LEÓN SÁNCHEZ  and
ANAND PILLAY
OMAR LEÓN SÁNCHEZ
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF MANCHESTER OXFORD ROAD MANCHESTER M13 9PL, UKE-mail: omar.sanchez@manchester.ac.uk
ANAND PILLAY
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME 255 HURLEY, NOTRE DAME IN 46556, USAE-mail: apillay@nd.edu
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Abstract

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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].

Keywords

03C6012H05model theorydifferential fieldsstrongly normal extensions
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 23 , Issue 2 , June 2017 , pp. 145 - 159
Copyright
Copyright © The Association for Symbolic Logic 2017 

References

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