Minimal Hales-Jewett Sets (Paperback)

A structure is Ramseyian if whenever it is divided into r classes, one of the classes exhibits properties similar to the whole structure. One of the concerns of Ramsey Theory is finding the smallest integer or set size for which a particular property holds. The Hales-Jewett Theorem is one of the major results of Ramsey Theory. In this work, the existence of minimal Hales-Jewett sets is established, and one is specifically identified.