Bochvar algebras: A categorical equivalence and the generated variety
Logic
2024-12-20 v1 Commutative Algebra
Category Theory
Abstract
The proper quasivariety BCA of Bochvar algebras, which serves as the equivalent algebraic semantics of Bochvar's external logic, was introduced by Finn and Grigolia in and extensively studied in a recent work by two of these authors. In this paper, we show that the algebraic category of Bochvar algebras is equivalent to a category whose objects are pairs consisting of a Boolean algebra and a meet-subsemilattice (with unit) of the same. Furthermore, we provide an axiomatisation of the variety $V(BCA) generated by Bochvar algebras. Finally, we axiomatise the join of Boolean algebras and semilattices within the lattice of subvarieties of V(BCA).
Cite
@article{arxiv.2412.14911,
title = {Bochvar algebras: A categorical equivalence and the generated variety},
author = {Stefano Bonzio and Francesco Paoli and Michele Pra Baldi},
journal= {arXiv preprint arXiv:2412.14911},
year = {2024}
}