4 papers
Third-order functionals on partial combinatory algebras
Jetze Zoethout
Computability relative to a partial function on the natural numbers can be formalized using the notion of an oracle for this function . This can be generalized to arbitrary…
On the Existence of Pushouts of Realizability Toposes
Jetze Zoethout
We consider two preorder-enriched categories of ordered PCAs: , where the arrows are functional morphisms, and , where the arrows are applicative morph…
Internal Partial Combinatory Algebras and their Slices
Jetze Zoethout
A partial combinatory algebra (PCA) is a set equipped with a partial binary operation that models a notion of computability. This paper studies a generalization of PCAs, introduced…
Provability Logic and the Completeness Principle
Albert Visser, Jetze Zoethout
In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with…