  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 $2\le
s<t$. Extending the problem of determining Ramsey numbers they defined the
numbers $$ f_{s,t}(n)=\min \big{\{} \max \{|W| : W\subseteq V(G) \text{and}
G[W] \text{contains no} K_s\}\big{\}}, $$ where the minimum is taken over all
$K_t$-free graphs $G$ of order $n$. In this note, we study an analogous
function $f_{s,t}^{(3)}(n)$ for 3-uniform hypergraphs. In particular, we show
that there are constants $c_1$ and $c_2$ depending only on $s$ such that $$
c_1(\log n)^{1/4} \left(\frac{\log\log n}{\log\log\log n}\right)^{1/2} < f_{s,
s+1}^{(3)}(n) < c_2 \log n. $$
