An invitation to model-theoretic galois theory

Bulletin of Symbolic Logic 16 (2):261 - 269 (2010)
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Abstract

We carry out some of Galois' work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions F ≤ K ≤ L. This exposition of a special case of [10] has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.

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2011-05-29

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Citations of this work

Model theoretic dynamics in Galois fashion.Daniel Max Hoffmann - 2019 - Annals of Pure and Applied Logic 170 (7):755-804.
Some definable galois theory and examples.Omar León Sánchez & Anand Pillay - 2017 - Bulletin of Symbolic Logic 23 (2):145-159.

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References found in this work

Une théorie de galois imaginaire.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (4):1151-1170.
Remarks on galois cohomology and definability.Anand Pillay - 1997 - Journal of Symbolic Logic 62 (2):487-492.
Remarks on Galois Cohomology and Definability.Anand Pillay - 1997 - Journal of Symbolic Logic 62 (2):487-492.

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