$Q$-universal quasivarieties of algebras

Universal Quasivarieties of Algebras

Two different notions of universal, one due to Hedrlín and Pultr in the 1960s and the other due to Sapir in the 1980s, are discussed, as well as the relationship between them. Some of the historical perspective and mathematical motivation lying behind them is also included, together with a brief overview of a variety meriting further investigation in this context.

Ideals in Quasivarieties of Algebras

On Certain Quasivarieties of Quasi-MV Algebras

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present pape...

Weak alg-universality and Q-universality of semigroup quasivarieties

In an earlier paper, the authors showed that standard semigroups M1, M2 andM3 play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by M2 and M3 are neither relatively alg-universal nor Q-universal, while there do exist finite semigroups S2 and S3 generating the same semigroup variety as M2 and ...

Quasivarieties and varieties of ordered algebras: regularity and exactness

We characterise quasivarieties and varieties of ordered algebras categorically in terms of regularity, exactness and the existence of a suitable generator. The notions of regularity and exactness need to be understood in the sense of category theory enriched over posets. We also prove that finitary varieties of ordered algebras are cocompletions of their theories under sifted colimits (again, i...