A universal domain technique for profinite posets

Abstract

We introduce a category of what we call profinite domains. This category of domains differs from most of the familiar ones in having a categorical coproduct as well as being cartesian closed. Study of these domains is carried out through the use of an equivalent category of pre-orders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous functors. Necessary conditions for the existence of such solutions are also given and used to derive results about solutions of some important equations. A new universal bounded complete domain is also demonstrated using a functor which has bounded complete domains as its fixed points.