On structural completeness versus almost structural completeness problem: a discriminator varieties case study

CAMPERCHOLI, MIGUEL; STRONKOWSKI, MICHAL; VAGGIONE, DIEGO

LOGIC JOURNAL OF THE IGPL (PRINT)

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2014 vol. 23 p. 235 - 246

1367-0751

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.