It is perhaps evident from several places of this volume that Ramsey theorem played a decisive role in Erdős’ combinatorial activity. And perhaps no other part of combinatorial mathematics is so dear to him as Ramsey theory and extremal problems. He was not creating or even aiming for a theory. However, a complex web of results and conjectures did, in fact, give rise to several theories. They all started with modest short papers by Erdős, Szekeres and Turán in the thirties. How striking it is to compare these initial papers with the richness of the later development, described, E.g., by the survey articles of Miki Simonovits (extremal graph theory) and Jeff Kahn (extremal set theory). In addition, the editors of these volumes tried to cover in greater detail the development of Ramsey theory mirrored and motivated by Erdős’ papers. In a way (and this certainly is one of the leitmotivs of Erdős’ work), there is little difference between, say, density Ramsey type results and extremal problems.
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