Ramsey Algebras: A Ramseyan Combinatorics For Universal Algebras - Teoh, Zu Yao (2018)
The study of Ramsey algebras is a Ramseyan-type study on algebras. The precise formulation of a Ramsey algebra is based on the work of Carlson on topological Ramsey spaces, from which a wide array of classical combinatorial results such as the Ellentuck theorem and Hindman’s theorem can be derived. After his groundbreaking work on Ramsey spaces, Carlson suggested that, for spaces that are generated by algebras, one may pursue a purely combinatorial study of these spaces, where results of topological nature can be derived from their associated combinatorial results. Such a direction of study would then be known as Ramsey algebra. The suggestion was first pursued by Teh in his doctoral work and some basic results concerning homogeneous algebras were obtained.