Caroline Terry : Some new logical zero-one laws

Posted by Kostyantyn Slutskyy , part of the Logic Seminar.

At

Oct. 13, 2015, 4 p.m.

In

SEO 427

Abstract

Suppose $\mathcal{L}$ is a finite first-order language and for each integer $n$, suppose $F(n)$ is a set of $\mathcal{L}$-structures with underlying set $\{1,\ldots, n\}$. We say the family $F=\bigcup_{n\in \mathbb{N}}F(n)$ has a zero-one law if for every first order sentence $\phi$, the proportion of elements in $F(n)$ which satisfy $\phi$ goes to zero or one as $n\rightarrow \infty$. In this talk we give a brief overview of the history of this topic, then present some new examples of families with zero-one laws. This is joint work with Dhruv Mubayi.