Year: 2025
Type: article
Abstract: This paper focuses on the structurally complete extensions of the system R $\mathbf {R}$ bold upper R -mingle ( RM $\mathbf {RM}$ bold upper R upper M ). The main theorem demonstrates that the set of all hereditarily structurally complete extensions of RM $\mathbf {RM}$ bold upper R upper M is countably infinite and forms an almost-chain, with only one branching element. As a corollary, we show that the set of structurally complete extensions of RM $\mathbf {RM}$ bold upper R upper M that are not hereditary is also countably infinite and forms a chain. Using algebraic methods, we provide a complete description of both sets. Furthermore, we offer a characterization of passive structural completeness among the extensions of RM $\mathbf {RM}$ bold upper R upper M : specifically, we prove that a quasivariety of Sugihara algebras is passively structurally complete if and only if it excludes two specific algebras. As a corollary, we give an additional characterization of quasivarieties of Sugihara algebras that are passively structurally complete but not structurally complete. We close the paper with a characterization of actively structurally complete quasivarieties of Sugihara algebras.
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2025.20
Author: KRZYSZTOF A. KRAWCZYK
Institution: Jagiellonian University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4408207533