erdos_564

Let $R_3(n)$ be the minimal $m$ such that if the edges of the $3$-uniform hypergraph on $m$ vertices are $2$-coloured then there is a monochromatic copy of the complete $3$-uniform hypergraph on $n$ vertices. Is there some constant $c>0$ such that $$ R_3(n) \geq 2^{2^{cn}}? $$

theorem erdos_564 : answer(sorry) ↔
    ∃ c > 0, ∀ᶠ n in atTop, (2 : ℝ)^(2 : ℝ)^(c * n) ≤ hypergraphRamsey 3 n

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