Bochvar algebras: A categorical equivalence and the generated variety

The proper quasivariety BCA of Bochvar algebras, which serves as the equivalent algebraic semantics of Bochvar’s external logic, was introduced by Finn & Grigolia [11] and extensively studied in [8]. 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).