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An Invitation to Model-Theoretic Galois Theory

Published online by Cambridge University Press:  15 January 2014

Alice Medvedev  and
Ramin Takloo-Bighash
Alice Medvedev
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, IL 60607-7045, USA E-mail:, alice@math.uic.edu, E-mail:, rtakloo@math.uic.edu
Ramin Takloo-Bighash
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, IL 60607-7045, USA E-mail:, alice@math.uic.edu, E-mail:, rtakloo@math.uic.edu
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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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Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 16 , Issue 2 , June 2010 , pp. 261 - 269
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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