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On congruence modularity in varieties of logic

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Abstract.

An open problem in algebraic logic asks whether a variety that is the equivalent algebraic semantics of an algebraizable logic must be congruence modular. A negative solution is provided here: it is shown that such ‘varieties of logic’ need satisfy no special congruence lattice identity.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045, USA, e-mail: wjb@uic.edu, , , , , , US

    W. J. Blok

  2. School of Mathematical and Statistical Sciences, University of Natal, King George V Avenue, Durban 4001, South Africa, e-mail: raftery@nu.ac.za, , , , , , ZA

    J. G. Raftery

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  1. W. J. Blok
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  2. J. G. Raftery
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Received June 15, 1999; accepted in final form July 10, 2000.

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Blok, W., Raftery, J. On congruence modularity in varieties of logic. Algebra univers. 45, 15–21 (2001). https://doi.org/10.1007/s000120050198

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  • DOI: https://doi.org/10.1007/s000120050198

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