Notions of size in partial semigroups
by
Jillian McLeod
Howard University

There are several natural notions of size in a discrete semigroup S that arise from notions of topological dynamics. Among these are the notions of thick , syndetic , piecewise syndetic , and central . These notions all have simple characterizations in terms of the algebra of \betaS, the Stone-Cech compactification of S.

A partial semigroup is, loosely speaking, a set together with a partiallly defined binary operation which is associative when it is defined. These have arisen in the applications of the algebra of the Stone-Cech compactification to Ramsey Theory. If a partial semigroup S is adequate , then there is a subset \deltaS of \betaS which is a compact right topological semigroup. In particular, analogues of the algebraic characterizations of each of the above notions of size all make sense in \deltaS. We derive combinatorial characterizations of each of these analogous notions, except central, and investigate the relations that hold among them.

Date received: June 2, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-37.