Logic Seminar
Caroline Terry
UIC
Some new logical zero-one laws
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.
Tuesday October 13, 2015 at 4:00 PM in SEO 427