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Random hypergraphs in pseudofinite fields

Part of: Model theory Connections with logic Graph theory

Published online by Cambridge University Press:  03 June 2009

Özlem Beyarslan
Özlem Beyarslan
Affiliation:
Boǧaziçi University, 34342 Bebek, Istanbul, Turkey (ozlem.beyarslan@boun.edu.tr)
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Abstract

We prove that n-hypergraphs can be interpreted in e-free perfect PAC fields in particular in pseudofinite fields. We use methods of function field arithmetic, more precisely we construct generic polynomials with alternating groups as Galois groups over a function field.

Keywords

pseudofinite fieldrandom graphrandom hypergraphfunction fieldGalois group

MSC classification

Secondary: 12L12: Model theory 05C80: Random graphs 03C60: Model-theoretic algebra
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 1 , January 2010 , pp. 29 - 47
Copyright
Copyright © Cambridge University Press 2010

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References

1.Abhyankar, S., Galois theory on the line in nonzero characteristic, Bull. Am. Math. Soc. 27(1) (1992), 68–133.CrossRefGoogle Scholar
2.Abhyankar, S., Alternating group coverings of the affine line for characteristic greater than two, Math. Annalen 296 (1993), 63–68.CrossRefGoogle Scholar
3.Abhyankar, S., Ou, J. and Sathaye, A., Alternating group coverings of the affine line for characteristic two, >Discr. Math. 133 (1994), 25–46.CrossRefGoogle Scholar
4.Ax, J., The elementary theory of finite fields, Annals Math. 88 (1968), 239–271.CrossRefGoogle Scholar
5.Bélair, L. et al. (eds), Model theory and applications, Quaderni di Mathematica, Volume 11 (Seconda Universita di Napoli, 2002).Google Scholar
6.Bollobás, B., Random graphs, Cambridge Studies in Advanced Mathematics, Volume 73 (Cambridge University Press, 2001).CrossRefGoogle Scholar
7.Duret, J.-L., Les corps faiblement algébriquement clos non séparablement clos ont la propriété d'indépendance, in Model theory of algebra and arithmetic, Lecture Notes in Mathematics, Volume 843, 135–157 (Springer, 1980).Google Scholar
8.Fried, M., Jarden, M., Field arithmetic, Ergodic Mathematics, Volume 11 (Springer, 2005).CrossRefGoogle Scholar
9.Fulton, W., Young tableaux, London Mathematical Society Student Texts, Volume 35 (Cambridge University Press, 1997).Google Scholar
10.Hodges, W., Model theory, Encyclopedia of Mathematics and Its Applications, Volume 42 (Cambridge University Press, 1993).CrossRefGoogle Scholar
11.Hrushovski, E., Pseudo-finite fields and related structures, in Model theory and applications (ed. Bélair, L. et al .), pp. 151–212, Quaderni di Mathematica, Volume 11 (Seconda Universita di Napoli, 2002).Google Scholar
12.Lang, S., Introduction to algebraic geometry (Addison-Wesley, Reading, MA, 1972).Google Scholar
13.Marker, D., Model theory: an introduction, Graduate Texts in Mathematics (Springer, 2002).Google Scholar
14.Serre, J. P., Topics in Galois theory, Research Notes in Mathematics, Volume 1 (Jones and Bartlett, Boston, MA, 1992).Google Scholar
15.Stichtenoth, H., Algebraic function fields and codes, Universitext (Springer, 1993).Google Scholar