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 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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Main Authors: | Campercholi, Miguel Alejandro Carlos, Stronkowski, Michal M., Vaggione, Diego José |
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Format: | submittedVersion biblioteca |
Language: | eng |
Published: |
2015
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Subjects: | Structural completeness, Almost structural completeness, Discriminator varieties, Semisimple quasivarieties, Minimal varieties, Minimal quasivarieties, |
Online Access: | http://hdl.handle.net/11086/20551 https://doi.org/10.1093/jigpal/jzu032 |
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