Relative congruence formulas and decompositions in quasivarieties
Loading...
Date
Authors
Campercholi, M.A.
Raftery, James G.
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
Quasivarietal analogues of uniform congruence schemes are discussed, and their 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⊆K, we supply some conditions under which M is the restriction to K of a variety, assuming that K has EDPRC.
Description
Keywords
Equational definability of principal relative congruences (EDPRC), Quasivariety, Filtral, Semisimple, Ideal, Inconsistency lemma
Sustainable Development Goals
Citation
Campercholi, M.A. & Raftery, J.G. Relative congruence formulas and decompositions in quasivarieties. Algebra universalis. (2017) 78: 407-425. https://doi.org/10.1007/s00012-017-0455-y.