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AN INVITATION TO MODEL-THEORETIC GALOIS THEORY
ALICE MEDVEDEV and RAMIN TAKLOO-BIGHASH
The Bulletin of Symbolic Logic
Vol. 16, No. 2 (JUNE 2010), pp. 261-269
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/27805178
Page Count: 9
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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  has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.
The Bulletin of Symbolic Logic © 2010 Association for Symbolic Logic