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ON THE STRUCTURE OF BOCHVAR ALGEBRAS
- Part of
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- Journal:
- The Review of Symbolic Logic / Volume 18 / Issue 1 / March 2025
- Published online by Cambridge University Press:
- 09 May 2024, pp. 273-299
- Print publication:
- March 2025
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- Article
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Bochvar algebras consist of the quasivariety
$\mathsf {BCA}$ playing the role of equivalent algebraic semantics for Bochvar (external) logic, a logical formalism introduced by Bochvar [4] in the realm of (weak) Kleene logics. In this paper, we provide an algebraic investigation of the structure of Bochvar algebras. In particular, we prove a representation theorem based on Płonka sums and investigate the lattice of subquasivarieties, showing that Bochvar (external) logic has only one proper extension (apart from classical logic), algebraized by the subquasivariety 
$\mathsf {NBCA}$ of 
$\mathsf {BCA}$. Furthermore, we address the problem of (passive) structural completeness ((P)SC) for each of them, showing that 
$\mathsf {NBCA}$ is SC, while 
$\mathsf {BCA}$ is not even PSC. Finally, we prove that both 
$\mathsf {BCA}$ and 
$\mathsf {NBCA}$ enjoy the amalgamation property (AP).
