On Deuber's partition theorem for (m, p, c)-sets

In 1973, Deuber published his famous proof of Rado’s conjecture regarding partition regular sets. In his proof, he invented structures called (m, p, c)-sets and gave a partition theorem for them based on repeated applications of van der Waerden’s theorem on arithmetic progressions. In this paper, we give the complete proof of Deuber’s, however with the more recent parameter set proof of his partition result for (m, p, c)-sets. We then adapt this parameter set proof to show that for any k,m, p, c, every Kk-free graph on the positive integers contains an (m, p, c)-set, each of whose rows are independent sets.