## Logic Seminar

Jan HubičkaCharles University
Big Ramsey degrees of hypergraphs
Wednesday, September 25, 2019 - 4:00pm
Malott 206

Given a countably infinite hypergraph $R$ and a finite hypergraph $A$, the big Ramsey degree of $A$ in $R$ is the least number $L$ such that, for every finite $k$ and every $k$-colouring of the embeddings of $A$ to $R$, there exists an embedding $f$ from $R$ to $R$ such that all the embeddings of $A$ to the image $f(R)$ have at most $L$ different colours.

We will discuss the results of Devlin and Sauer on, respectively, big Ramsey degrees of the order of the rationals and the countably infinite random graph. We will discuss how these results can be further generalized to hypergraphs and relational structures.