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Coding complete theories in Galois groups

Published online by Cambridge University Press:  12 March 2014

James Gray*
Affiliation:
School of Mathematics, The University of Edinburgh, James Cleric Maxwell Building, The King's Buildings, Edinburgh EH9 3JZ, UK, URL: http://www.wjagray.co.uk/maths, E-mail: [email protected]

Abstract

In this paper, I will give a new characterisation of the spaces of complete theories of pseudofinite fields and of algebraically closed fields with a generic automorphism (ACFA) in terms of the Vietoris topology on absolute Galois groups of prime fields.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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References

REFERENCES

[1]Ax, James, Solving diophantine problems modulo every prime, Annals of Mathematics, vol. 85 (1967), pp. 161183.CrossRefGoogle Scholar
[2]Ax, James, The elementary theory of finite fields, Annals of Mathematics, vol. 88 (1968), pp. 239271.CrossRefGoogle Scholar
[3]Cassels, J. W. S. and Fröhlich, A. (editors), Algebraic number theory, Academic Press, 1967.Google Scholar
[4]Chatzidakis, Zoé and Hrushovski, E., Model theory of difference fields, Transactions of the American Mathematical Society, vol. 351 (1999), pp. 29973071.CrossRefGoogle Scholar
[5]Denef, Jan and Loeser, F., Definable sets, motives and p-adic integrals, Journal of the American Mathematical Society, vol. 14 (2000), pp. 429469.CrossRefGoogle Scholar
[6]Fried, Michael D. and Jarden, Moshe, Field arithmetic, Modern Surveys in Mathematics, vol. 11, Springer-Verlag, 1986.CrossRefGoogle Scholar
[7]Gray, William James Andrew, Coding complete theories in galois groups, Ph.D. thesis, University of Edinburgh, 2004.Google Scholar
[8]Iwasawa, Kenkichi, On Galois groups of local fields, Transactions of the American Mathematical Society, vol. 80 (1955), no. 2, pp. 448469.CrossRefGoogle Scholar
[9]Johnstone, Peter T., Stone spaces, Cambridge studies in advanced mathematics, no. 3, Cambridge University Press, 1982.Google Scholar
[10]Kelly, John L., General topology, The University Series in Higher Mathematics, D. Van Nostrand Company, Inc., 1955.Google Scholar
[11]Kiefe, Catarina, Sets definable over finite fields: Their zeta-functions, Transactions of the American Mathematical Society, vol. 223 (1976), pp. 4559.CrossRefGoogle Scholar
[12]Koenigsmann, Jochen, From p-rigid elements to valuations {with a Galois-characterization of p-adic fields), Journal für die reine und angewandte Mathematik, vol. 465 (1995), pp. 165182.Google Scholar
[13]Macintyre, Angus, Generic automorphisms of fields, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 165180.CrossRefGoogle Scholar
[14]Michael, Ernest, Topologies on spaces of subsets, Transactions of the American Mathematical Society, vol. 71 (1951), pp. 152182.CrossRefGoogle Scholar
[15]Neukirch, Jürgen, Schmidt, Alexander, and Wingberg, Kay, Cohomology of number fields, A Series of Comprehensive Studies in Mathematics, vol. 323, Springer, 2000.Google Scholar
[16]Simmons, H., Existentially closed structures, this Journal, vol. 37 (1972), pp. 293310.Google Scholar
[17]Vietoris, Leopold, Bereiche zweiter Ordnung, Monatshefte für Mathematik und Physik, vol. 32 (1922), pp. 258280.CrossRefGoogle Scholar
[18]Wilson, John S., Profinite groups, London Mathematical Society Monographs New Series, no. 19, Oxford University Press, 1998.CrossRefGoogle Scholar