Bochvar algebras: A categorical equivalence and the generated variety

Abstract

The proper quasivariety $\mathsf{BCA}$ of Bochvar algebras, which serves as the equivalent algebraic semantics of Bochvar's external logic, was introduced by Finn & Grigolia (1993) and extensively studied in (Bonzio & Pra Baldi, 2025). 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 $V(\mathsf{BCA})$ generated by Bochvar algebras. Finally, we axiomatise the join of Boolean algebras and semilattices within the lattice of subvarieties of $V(\mathsf{BCA})$.