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Fibring: completeness preservation

Published online by Cambridge University Press:  12 March 2014

Alberto Zanardo ,
Amilcar Sernadas  and
Cristina Sernadas
Alberto Zanardo
Affiliation:
Dipartimento di Matematica Pura ed Applicata, University of Padova, Italy, E-mail: azanardo@math.unipd.it
Amilcar Sernadas
Affiliation:
CMA, Departamento de Matematica, 1st, Portugal, E-mail: acs@math.ist.utl.pt
Cristina Sernadas
Affiliation:
CMA, Departamento de Matemática, 1st, Portugal, E-mail: css@math.ist.utl.pt
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Abstract

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 414 - 439
Copyright
Copyright © Association for Symbolic Logic 2001

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