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From Sets and Types to Topology and AnalysisTowards practicable foundations for constructive mathematics$
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Laura Crosilla and Peter Schuster

Print publication date: 2005

Print ISBN-13: 9780198566519

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566519.001.0001

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PRESHEAF MODELS FOR CONSTRUCTIVE SET THEORIES

PRESHEAF MODELS FOR CONSTRUCTIVE SET THEORIES

Chapter:
(p.62) 4 PRESHEAF MODELS FOR CONSTRUCTIVE SET THEORIES
Source:
From Sets and Types to Topology and Analysis
Author(s):

Nicola Gambino

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566519.003.0004

This chapter introduces new kinds of models for constructive set theories based on categories of presheaves. It concentrates on categories of classes rather than sets, following the lines of algebraic set theory. It defines a general notion of what is a categorical model for CST, and shows that categories of presheaves provide examples of such models. To do so, it considers presheaves as functors with values in a category of classes. The models introduced are a counterpart of the presheaf models for intuitionistic set theories defined by Dana Scott in the 1980s. In this work, the author has to overcome the challenges intrinsic to dealing with generalized predicative formal systems rather than impredicative ones. An application to an independence result is discussed.

Keywords:   presheaves, algebraic set theory, intuitionistic set theory, independence proofs, Dana Scott

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