### Abstract

In this paper we address the problem of solving recursive domain equations
using uncountable limits of domains. These arise for instance, when
dealing with the omega-1 continuous function-space constructor and
are used in the denotational semantics of
programming languages which feature unbounded choice constructs.
Surprisingly, the category of cpo's and omega-1 continuous embeddings is
not omega-0 cocomplete.
Hence the standard technique for solving reflexive domain equations fails.
We give two alternative methods.
We discuss also the issue of completeness of the lambda-beta-eta-calculus
w.r.t reflexive domain models. We show that among the
reflexive domain models in the category of cpo's and omega-0 continuous
functions there is one which has a minimal theory.
We give a reflexive domain model in the category of cpo's and
omega-1 continuous functions whose theory is precisely the
lambda-beta-eta theory.
So omega-1 continuous lambda-models are complete for the lambda-beta-eta
calculus.