Summary: Sheaf Toposes for Realizability
Steven Awodey 
Philosophy Department
Carnegie Mellon University
Andrej Bauer y
Institut Mittag-Leer
The Royal Swedish Academy of Sciences
April 10, 2001
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 dierent 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 work is to compare realizability models over partial com-
binatory algebras by embedding them into sheaf toposes. We then use the
machinery of Grothendieck toposes and geometric morphisms to study the

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

Collections: Mathematics