Ozlem Beyarslan : Pseudofinite fields and random graphs

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Oct. 25, 2005, 4 p.m.

In

SEO 427

Abstract

A pseudofinite field is an infinite field satisfying all first-order properties which hold in all finite fields. Pseudofinite fields exist and they can be realized, for example, as ultraproducts of finite fields. An $n$-ary random graph is a set $X$ with a symmetric and irreflexive $n$-ary relation $R$ such that for any two finite and disjoint subsets $A$ and $B$ of $X^{n-1}$, there is an $x\in X$ such that $R(a,x) $ and $\neg R(b,x)$ for all $a\in A$ and $b\in B$. In 1980 J. L. Duret interpreted a random binary graph in a pseudofinite field. This has some important model theoretic consequences. We will show that we can interpret a random $n$-ary graph in pseudofinite fields.