RAMSEY ORDERLY ALGEBRAS AS A NEW APPROACH TO RAMSEY ALGEBRAS

Wen Chean Teh; Zu Yao Teoh

Wen Chean Teh
Zu Yao Teoh

Keywords: Ramsey algebra, Ramsey orderly algebra, Ramsey space, orderly term, Ellentusk's Space, Hindman’s Theorem

Abstract

Ramsey algebras are algebras that induce Ramsey spaces, which are generalizations of the Ellentuck space and the Milliken space. Previous work has suggested a possible local version of Ramsey algebras induced by infinite sequences. We formulate this local version and call it Ramsey orderly algebra. In this paper, we present an introductory treatment of this new notion and provide justification for it to be a sound approach for further study in Ramsey algebras. The main connection is that an algebra is Ramsey if and only if each of its induced orderly algebra is Ramsey.