Logic Seminar

Abstract: Henson's family of countable homogeneous-universal $K_n$-free graphs, $n\ge 3$, has been widely studied in model theory.  Less well studied are the existentially complete, countable universal $B_{n,3}$--free graphs, where $B_{n,3}$ is the graph on $n+2$ vertices consisting of a $K_n$ and a triangle joined at one vertex.  These graphs were shown to exist by Komjath (for $n=3$, the `bowtie') and by Cherlin, Shelah and Shi (for $n \ge 4$).  In this talk I will describe the structure of these graphs, and present some new and old results, due to myself and others, about their model-theoretic properties.