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A SYNTACTIC CHARACTERIZATION OF MORITA EQUIVALENCE

Published online by Cambridge University Press:  09 January 2018

DIMITRIS TSEMENTZIS
DIMITRIS TSEMENTZIS*
Affiliation:
DEPARTMENT OF PHILOSOPHY PRINCETON UNIVERSITY PRINCETON, NJ08544, USAE-mail:dtsement@princeton.edu
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Abstract

We characterize Morita equivalence of theories in the sense of Johnstone in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson for cartesian, regular, coherent, geometric and first-order theories. This provides a purely syntactic characterization of the relation between two theories that have equivalent categories of models naturally in any Grothendieck topos.

Keywords

Primary 03G3018B25Secondary 03C52classifying toposesMorita equivalencecommon definitional extension
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 4 , December 2017 , pp. 1181 - 1198
Copyright
Copyright © The Association for Symbolic Logic 2017 

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