Sharp thresholds for hypergraph regressive Ramsey numbers (Q618311)

The authors determine the growth-rate of the regressive Ramsey numbers for hypergraphs, with dependence on the growth-rate of the parameter function \(f\). These growth-rates are measured via the the fast-growing Hardy functions \(F_\alpha\) indexed by towers of exponentiation in base \(\omega\). Their results give a sharp classfication for hypergraphs of arbitrary dimension of the thresholds at which the \(f\)-regressive Ramsey numbers undergoe a drastical change in growth-rate, extending results similar results for graphs in the work of Lee, Kojman, Omri and Weiermann.