English

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}
}
R2 v1 2026-06-23T07:38:12.382Z