  Motivated by the Erdos-Szekeres convex polytope conjecture in $R^d$, we
initiate the study of the following induced Ramsey problem for hypergraphs.
Given integers $ n > k \geq 5$, what is the minimum integer $g_k(n)$ such that
any $k$-uniform hypergraph on $g_k(n)$ vertices with the property that any set
of $k + 1$ vertices induces 0, 2, or 4 edges, contains an independent set of
size $n$. Our main result shows that $g_k(n) > 2^{cn^{k-4}}$, where $c = c(k)$.
