On structural completeness versus almost structural completeness problem: A discriminator varieties case study
Miguel A. Campercholi, Michał M. Stronkowski, D. Vaggione · Logic Journal of IGPL · 2014
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.