In Berline&Grue-97 it was shown that (in short) all kappa-Scott domains
that satisfy a certain domain equation are models of map theory.
The talk shows that the Dedekind Cut construction, which allows to construct the real numbers from the rational ones, can be applied to kappa-Scott domains, yielding new and interesting models of map theory. When applied to the model constructed in Berline&Grue-97, the result is a model of a version of map theory, that has much simpler axioms than the original version.
The talk focuses on the Dedekind cut construction and its properties.