Relative congruence formulas and decompositions in quasivarieties

CAMPERCHOLI, MIGUEL; RAFTERY, JAMES

ALGEBRA UNIVERSALIS

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2017

0002-5240

Quasivarietal analogues of uniform congruence schemes are discussed, andtheir relationship with the equational definability of principal relative congruences (EDPRC) is established, along with their significance for relative congruences on subalgebras of products. Generalizing the situation in varieties, we prove that a quasivariety is relatively ideal iff it has EDPRC; it is relatively filtral iff it is relatively semisimple with EDPRC. As an application, it is shown that a finitary sentential logic, algebraized by a quasivariety K, has a classical inconsistency lemma if and only if K is relatively filtral and the subalgebras of its nontrivial members are nontrivial. A concrete instance of this result is exhibited, in which K is not a variety. Finally, for quasivarieties M