Local Realizability Toposes and a Modal Logic for Computability: (Extended Abstract)

✍ Scribed by Steven Awodey; Lars Birkedal; Dana S. Scott

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 718 KB
• Volume: 23
• Category: Article
• ISSN: 1571-0661
• DOI: 10.1016/s1571-0661(04)00101-x

✦ Synopsis

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, w e i n vestigate a con guration of three toposes, which w e regard as describing a notion of relative computability. A ttention is focussed on a certain local map of toposes, which w e study rst 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.