The finite big Ramsey degrees of Henson graphs are provable in ${\mathrm{ACA}}_0$

Peter Cholak, Natasha Dobrinen, Henry Towsner

Let ${\mathbb{H}}_{n+1}$ denote a computable copy of the $(n+1)$-clique free universal homogeneous Henson graph, $G$ denote a finite subgraph of ${\mathbb{H}}_{n+1}$, and $k(G,n)$ deno…