file.pdf (816.32 kB)
0/0

Local Realizability Toposes and a Modal Logic for Computability

Download (816.32 kB)
journal contribution
posted on 01.01.2000 by Steven Awodey, Lars Birkedal, Dana Scott
This work is a step toward the development of a logic for types and computation that includes not only the usual spaces of mathematics and constructions, but also spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes that we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we first study axiomatically, and then by deriving a modal calculus as its internal logic. The resulting framework is intended as a setting for the logical and categorical study of relative computability.

Categories

Keyword(s)

History

Publisher Statement

All Rights Reserved

Date

01/01/2000

Exports

Categories

Keyword(s)

Exports