There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank ω CK 1 + 1. Makkai [12] produced a structure of Scott rank ω CK 1 , which can be made computable [10], and simplified so that it is just a tree [4]. In the present paper, we show that there are further computable str...

In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cech-complete. An important consequence is that any metric space homeomorphic to the maximal elements of a Scott domain must be completely metrizable.

The paper considers algebraic directed-complete partial orders with a semi-regular Scott topology, called regular domains. As is well known, the category of Scott domains and continuous maps is Cartesian closed. This is no longer true, if the domains are required to be regular. Two Cartesian closed subcategories of the regular Scott domains are exhibited: regular dI-domains with stable maps and...

We investigate when the space OX of open subsets of a topological space X endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of X, which in turn is characterized in terms of coincidence of the Scott topology of OX ×OX with the product of the Scott topologies of OX at (X,X). On the other hand, we characterize diagonality of OX endowed with ...