An invitation to model-theoretic Galois theory
Logic
2010-08-24 v3 Commutative Algebra
History and Overview
Abstract
We carry out some of Galois's 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. This exposition of a special case of Poizat's "Une th\'eorie de Galois imaginaire." (1983) has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.
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Cite
@article{arxiv.0909.4340,
title = {An invitation to model-theoretic Galois theory},
author = {Alice Medvedev and Ramin Takloo-Bighash},
journal= {arXiv preprint arXiv:0909.4340},
year = {2010}
}
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