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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
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      dt: Dec2017
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      pub: Cambridge University Press
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        10.1017/jsl.2017.59
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        atl: A SYNTACTIC CHARACTERIZATION OF MORITA EQUIVALENCE.
      aug:
        au: TSEMENTZIS, DIMITRIS
        affil: DEPARTMENT OF PHILOSOPHY PRINCETON UNIVERSITY PRINCETON, NJ 08544, USA
      su:
        Topoi (Mathematics)
        Mathematical category theory
        Model theory
        Algorithmic randomness
        Applied mathematics
        Algebraic logic
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        subj:
          Topoi (Mathematics)
          Mathematical category theory
          Model theory
          Algorithmic randomness
          Applied mathematics
          Algebraic logic
      keyword:
        18B25
        classifying toposes
        common definitional extension
        Morita equivalence
        Primary 03G30
        Secondary 03C52
      ab: 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.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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          year: 2017
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