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Sheaf Toposes for Realizability Steven Awodey
 

Summary: Sheaf Toposes for Realizability
Steven Awodey
Philosophy Department
Carnegie Mellon University
Andrej Bauer
Department of Mathematics and Physics
University of Ljubljana
September 7, 2004
Abstract
We compare realizability models over partial combinatory algebras
by embedding them into sheaf toposes. We then use the machinery of
Grothendieck toposes and geometric morphisms to study the relation-
ship between realizability models over different partial combinatory
algebras. This research is part of the Logic of Types and Computa-
tion project at Carnegie Mellon University under the direction of Dana
Scott.
1 Introduction
The purpose of this paper is to compare realizability models over partial
combinatory algebras by embedding them into sheaf toposes. We then use
the machinery of Grothendieck toposes and geometric morphisms to study

  

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

 

Collections: Mathematics