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Workshop on Realizability Preliminary Version Local Realizability Toposes and a Modal Logic
 

Summary: Workshop on Realizability Preliminary Version
Local Realizability Toposes and a Modal Logic
for Computability
(Extended Abstract)
Steven Awodey 1
Department of Philosophy, Carnegie Mellon University
Lars Birkedal 1
School of Computer Science, Carnegie Mellon University
Dana S. Scott 1
School of Computer Science, Carnegie Mellon University
Abstract
This work is a step toward developing a logic for types and computation that in≠
cludes both the usual spaces of mathematics and constructions and spaces from
logic and domain theory. Using realizability, we investigate a configuration 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 first 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.
1 Introduction
We report here on the current status of research on the Logic of Types and

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University
Birkedal, Lars - Theory Department, IT-Universitetet i KÝbenhavn

 

Collections: Computer Technologies and Information Sciences; Mathematics