On generalized Ramsey numbers for 3-uniform hypergraphs

The well-known Ramsey number $r(t,u)$ is the smallest integer $n$ such that every $K_t$-free graph of order $n$ contains an independent set of size $u$. In other words, it contains a subset of $u$ vertices with no $K_2$. Erd{\H o}s and Rogers introduced a more general problem replacing $K_2$ by $K_s$ for $2\le s