It is well known that, although the category of topological spaces is not cartesian closed, it possesses many cartesian closed full subcategories, e.g.: (i) compactly generated Hausdorff spaces; (ii)… (More)

We present a simple and workable axiomatization of domain theory within intuitionistic set theory, in which predomains are (special) sets, and domains are algebras for a simple equational theory. We… (More)

We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes… (More)

We advocate a pragmatic approach to constructive set theory, using axioms based solely on set-theoretic principles that are directly relevant to (constructive) mathematical practice. Following this… (More)

We present two probabilistic powerdomain constructions in topological domain theory. The first is given by a free ”convex space” construction, fitting into the theory of modelling computational… (More)

We introduce a notion of Grothendieck logical relation and use it to characterise the deenability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus… (More)

We give a universal property for an “abstract probabilistic powerdomain” based on an analysis of observable properties of probabilistic computation. The universal property determines an abstract… (More)

We extend arithmetic with a new predicate Pr, giving axioms for Pr based on first-order versions of Lob's derivability conditions. We hoped that the addition of a reflection schema mentioning Pr… (More)

15 As far as we know, this approach is new and has never been proposed before. However, some comparisons with existing systems can nevertheless be made. The idea of a metatheory mapped directly from… (More)

We give a constructive proof that Baire space embeds in any inhabited locally non-compact complete separable metric space, X, in such a way that every sequentially continuous function from Baire… (More)