  We give a probabilistic construction of a $3$-uniform hypergraph on $N$
vertices with independence number $O(\log N / \log \log N)$ in which there are
at most two edges among any four vertices. This bound is tight and solves a
longstanding open problem of Erd\H{o}s and Hajnal in Ramsey theory. We further
extend this result to prove tight bounds on various other hypergraph Ramsey
numbers.
