标题： 博奇瓦尔代数：范畴等价性和生成的种类 显示英文标题

标题： Bochvar algebras: A categorical equivalence and the generated variety

摘要： 博赫瓦尔代数的适当拟簇BCA，作为博赫瓦尔外部逻辑的等价代数语义，由芬恩和格里戈利亚在……中引入，并在两位作者最近的一项工作中进行了深入研究。 在本文中，我们证明博赫瓦尔代数的代数范畴等价于一个对象为由一个布尔代数和同一对象的交子半格（带单位）组成的对的范畴。 此外，我们提供了由博赫瓦尔代数生成的流形\$V(BCA)的公理化。 最后，我们在V(BCA)的子流形格中对布尔代数和半格的并进行公理化。 显示英文摘要

摘要： 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).