Abstract
In 1930 Frank Plumpton Ramsey had written a paper On a problem in formal logic which initiated a part of discrete mathematics nowadays known as Ramsey Theory. At about the same time B.L. van der Waerden (1927) proved his famous Ramsey-type result on arithmetical progressions. A few years later Ramsey’s theorem was rediscovered by P. Erdős and G. Szekeres (1935) while working on a problem in geometry. In 1963 A.W. Hales and R.I. Jewett revealed the combinatorial core of van der Waerden’s theorem and proved a general result which turned this collection of separate ingenious results into Ramsey Theory. In the next three chapters we present some of the most basic facts of this theory.
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