The paper proves existence of strong Boolean Ramsey numbers R^#_k,t(B|Q) for any finite poset Q and gives probabilistic upper bounds plus combinatorial lower bounds on the strong Erdős-Gyárfás function f_t^#(n,p,q).
Erd˝ os, Solved and unsolved problems in combinatorics and combinatorial number theory, Eur
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Erd\H{o}s-Gy\'{a}rf\'{a}s problem for partially ordered sets
The paper proves existence of strong Boolean Ramsey numbers R^#_k,t(B|Q) for any finite poset Q and gives probabilistic upper bounds plus combinatorial lower bounds on the strong Erdős-Gyárfás function f_t^#(n,p,q).