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

Summary: Local Realizability Toposes and a Modal Logic for Computability
(Extended Abstract)
Steven Awodey 1 \Lambda Lars Birkedal 2y Dana S. Scott 2z
1 Department of Philosophy, Carnegie Mellon University
2 School of Computer Science, Carnegie Mellon University
April 15, 1999
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 in­
vestigate a configuration of three toposes, which we
regard as describing a notion of relative computabil­
ity. 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 computabil­
ity.
1 Introduction

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics