Logic Seminar
Ozlem Beyarslan
UIC
Pseudofinite fields and random graphs
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.
Tuesday October 25, 2005 at 4:00 PM in SEO 427