... proof of Theorem 28 of [4] can also be adapted to hereditary properties of tour-naments, to produce many properties with different exponential speeds, but we spare thereader the details. Of ... proof of Theorem 1.Lemma 7. Let P be a hereditary property of tournaments. If B(P) = ∞, then P containsarbitrarily large structures of Type 1 or 2.Proof. Let P be a hereditary property of ... Bollob´as, M. Saks and T. V. S´os, The diversity of graph properties, submitted.[6] J. Balogh, B. Bollob´as and D. Weinreich, The speed of hereditary properties of graphs, J. Combin. Theory Ser. B, 79...