A Powerdomain for Countable Non-determinism

This paper proposes a general powerdomain for countable nDndeterminism and uses it to give the denotational semantics of a simple imperative programming language with a fair parallel construct. As already known from the simple case of a discrete cpo [AP] countable nondeterminism seems to force the consideration of non-continuous functions. In the classical Scott-Strachey approach only continuous functions are allowed and it is necessary to extend the mathematics to a weaker kind of continuity and show how it is still possible to specify and work with least solutions to recursive equations for elements of domains and initial solutions to recursive domain equations.