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A SYNTACTIC CHARACTERIZATION OF MORITA EQUIVALENCE.

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...

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Published in:Journal of Symbolic Logic Vol. 82; no. 4; pp. 1181 - 1199
Main Author: TSEMENTZIS, DIMITRIS
Format: Article
Published: Cambridge University Press Dec2017
Subjects:
Topoi (Mathematics)
Mathematical category theory
Model theory
Algorithmic randomness
Applied mathematics
Algebraic logic
Online Access:View this record in EBSCOhost
Summary: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.