Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T21:08:55.085Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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