On structural completeness versus almost structural completeness problem : a discriminator varieties case study
Campercholi, Miguel Alejandro Carlos
Stronkowski, Michal M.
Vaggione, Diego José
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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.
Campercholi, M., Stronkowski, M. y Vaggione, D. (2015). On structural completeness versus almost structural completeness problem. [versión enviada para evaluación] ( Publicada posteriormente en Logic Journal of the Interest Group in Pure and Applied Logic, 23 (2), 235-246. https://doi.org/10.1093/jigpal/jzu032 )