On structural completeness versus almost structural completeness problem : a discriminator varieties case study
We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varie...
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| Autores principales: | , , |
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| Formato: | submittedVersion Fil: Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Fil: Stronkowski, Michal M. Warsaw University of Technology. Faculty of Mathematics and Information Sciences; Polonia. Fil: Fil: Vaggione, Diego José. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. article |
| Lenguaje: | Inglés |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/11086/20551 https://doi.org/10.1093/jigpal/jzu032 |
| Aporte de: |
| Sumario: | We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete. |
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