  Ramsey algebras are algebras that induce Ramsey spaces, which are
generalizations of the Ellentuck space and Milliken's space. Previous work
suggests a possible local version of Ramsey algebras induced by infinite
sequences. Hence, we introduce a new structure called orderly algebra. Under
our canonical setup, an algebra is Ramsey if and only if every of its induced
orderly algebra is Ramsey. In this paper, we present justifications for this
novel notion as a sound approach for further study on Ramsey algebras.
