Computability structures, simulations and realizability

Computability structures, simulations and realizability

We generalize the standard construction of realizability models (specifically, of categories of assemblies) to a wide class of computability structures, broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion of simulation between such computability structures, and show how these simulations correspond precisely to cer...

Ordered Structures and Computability Ordered Structures and Computability Dedication

We consider three questions surrounding computable structures and orderings. First, we make progress toward answering a question of Downey, Hirschfeldt, and Goncharov by showing that for a large class of countable linear orderings, the Turing degree spectrum of the successor relation is closed upward in the c.e. degrees. Next we consider computable partial orders (specifically, finitely branchi...

Workshop on Realizability Preliminary Version Local Realizability Toposes and a Modal Logic for Computability (extended Abstract)

This work is a step toward developing a logic for types and computation that includes both the usual spaces of mathematics and constructions and spaces from logic and domain theory. Using realizability, we investigate a connguration of three toposes, which we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we study rst axio...

Isometries and Computability Structures

We investigate the relationship between computable metric spaces (X, d, α) and (X, d, β), where (X, d) is a given metric space. In the case of Euclidean space, α and β are equivalent up to isometry, which does not hold in general. We introduce the notion of effectively dispersed metric space and we use it in the proof of the following result: if (X, d,α) is effectively totally bounded, then (X,...

Local Realizability Toposes and a Modal Logic for Computability