An invitation to model-theoretic Galois theory

Alice Medvedev; Ramin Takloo-Bighash

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arXiv · 0909.4340

An invitation to model-theoretic Galois theory

Alice Medvedev·Ramin Takloo-Bighash

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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 théorie 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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BibTeX RIS

Alice Medvedev, Ramin Takloo-Bighash. 2010-08-23. An invitation to model-theoretic Galois theory. https://arxiv.org/abs/0909.4340

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