Year: 2024
Type: article
Abstract: It is a classic result of Segerberg and Maksimova that a variety of S 4 $\mathsf {S4}$ sans serif upper S Baseline sans-serif 4 -algebras is locally finite iff it is of finite depth. Since the logic MS 4 $\mathsf {MS4}$ sans serif upper M upper S sans serif 4 (monadic S 4 $\mathsf {S4}$ sans serif upper S Baseline sans-serif 4 ) axiomatizes the one-variable fragment of QS 4 $\mathsf {QS4}$ sans serif upper Q upper S sans serif 4 (predicate S 4 $\mathsf {S4}$ sans serif upper S Baseline sans-serif 4 ), it is natural to try to generalize the Segerberg–Maksimova theorem to this setting. We obtain several results in this direction. Our positive results include the identification of the largest semisimple variety of MS 4 $\mathsf {MS4}$ sans serif upper M upper S sans serif 4 -algebras. We prove that the corresponding logic MS 4 S $\mathsf {MS4_S}$ sans serif upper M upper S sans serif 4 Subscript sans serif upper S has the finite model property. We show that both
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2024.89
Authors: GURAM BEZHANISHVILI, CHASE MEADORS
Institutions: New Mexico State University, University of Colorado Boulder
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: $3,450
OpenAlex ID: W4405689280