The Hales-Jewett theorem and its application to further generalisations of m, n, k-games
Marcus Näslund · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2013
An overview is given of main results of Ramsey Theory and especially of the finite Hales-Jewett theorem, along with Saharon Shelah’s proof, which implies and unites most of the content. With the aid of the Hales-Jewett theorem some ideas are discussed for applying the theory to refine the search for winning strategies in higher-dimensional generalisations of m,n, k-games. These games are in turn generalisations of the classic 3× 3 board game known as TicTacToe.