On prevarieties of logic

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Authors

Moraschini, Tommaso
Raftery, James G.

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Volume Title

Publisher

Springer

Abstract

It is proved that every prevariety of algebras is categorically equivalent to a ‘prevariety of logic’, i.e., to the equivalent algebraic semantics of some sentential deductive system. This allows us to show that no nontrivial equation in the language ∧,∨,∘ holds in the congruence lattices of all members of every variety of logic, and that being a (pre)variety of logic is not a categorical property.

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Keywords

Prevariety of logic, Algebraizable logic, Maltsev class

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Citation

Moraschini, T. & Raftery, J.G. On prevarieties of logic. Algebra universalis (2019) 80: 37. https://doi.org/10.1007/s00012-019-0611-7.