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math.CT2021
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…
math.CT2020
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…
math.CT2019
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…