Journal of Symbolic Logic

Fibring: Completeness Preservation

Alberto Zanardo, Amilcar Sernadas, and Cristina Sernadas

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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 logics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings.

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J. Symbolic Logic, Volume 66, Issue 1 (2001), 414-439.

First available in Project Euclid: 6 July 2007

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Zanardo, Alberto; Sernadas, Amilcar; Sernadas, Cristina. Fibring: Completeness Preservation. J. Symbolic Logic 66 (2001), no. 1, 414--439.

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