We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration
operator is defined embodying the equational properties of iteration theories. We prove a …

We study concrete sheaf models for a call-by-value higher-order language with recursion.
Our family of sheaf models is a generalization of many examples from the literature, such as …

This is the first of a series of three articles devoted to the conceptual problem of identifying
the natural notions of computability at higher types (over the natural numbers) and …

We motivate and define a category of topological domains, whose objects are certain
topological spaces, generalising the usual ω-continuous dcppos of domain theory. Our …

Toposes and quasi-toposes have been shown to be useful in mathematics, logic and
computer science. Because of this, it is important to understand the different ways in which …

We consider a notion of sequential functional of finite type, more generous than the familiar
notion embodied in Plotkin's language PCF. We study both the “full” and “effective” partial …

Synthetic domain theory (SDT) is a version of Domain Theory where 'all functions are
continuous'. Following the original suggestion of Dana Scott, several approaches to SDT …

We present a fully abstract model of a call-by-value language with higher-order functions,
recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by …

We relate certain models of Axiomatic Domain Theory (ADT) and Synthetic Domain Theory
(SDT). On the one hand, we introduce a class of non-elementary models of SDT and show …

We axiomatize a notion of" classic structure" on a regular category, isolating the essential
properties of the category of classes together with its full subcategory of sets. Like the …