The implementation and semantics of dependent type theories can be studied in a syntax-
independent way: the objective metatheory of dependent type theories exploits the universal …

Synthetic topology as conceived in this monograph has three fundamental aspects:(i) to
explain what has been done in classical topology in conceptual terms,(ii) to provide one …

It is well known that, although the category of topological spaces is not Cartesian closed, it
possesses many Cartesian closed full subcategories, eg:(i) compactly generated Hausdorff …

Image factorizations in regular categories are stable under pullbacks, so they model a
natural modal operator in dependent type theory. This unary type constructor [A] has turned …

The formal systems that are nowadays called λ-calculus and combinatory logic were both
invented in the 1920s, and their aim was to describe the most basic properties of function …

In this dissertation, I explore aspects of computable analysis and topology in the framework
of relative realizability. The computational models are partial combinatory algebras with …

Triposes were introduced as presentations of toposes by JME Hyland, PT Johnstone and
AM Pitts. They introduced a construction that, from a tripos P:C^op→Pos, produces an …

Abstract Stone Duality is a new paradigm for general topology in which computable
continuous functions are described directly, without using set theory, infinitary lattice theory …

A basic concept of Type Two Theory of Effectivity (TTE) is the notion of an admissibly
represented space. Admissibly represented spaces are closely related to qcb-spaces. The …

The formal systems that are nowadays called λ-calculus and combinatory logic were both
invented in the 1920s, and their aim was to describe the most basic properties of function …