On prevarieties of logic
Logic
2019-02-13 v1
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 "meet, join, and relational product" 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.
Keywords
Cite
@article{arxiv.1902.04160,
title = {On prevarieties of logic},
author = {T. Moraschini and J. G. Raftery},
journal= {arXiv preprint arXiv:1902.04160},
year = {2019}
}