Quasivarieties of logic, regularity conditions and parameterized algebraization (Q1422448)

The authors exploit the many formal similarities between quasivarieties of logic and relatively congruence-regular quasivarieties. Indeed, they develop a unifying model for them which extends the Blok-Pigozzi theory of algebraizable deductive systems. The development includes the detailed proof of many theorems, the presentation of several useful examples of the results, an important counterexample (a quasivariety need not be \(t\)-deductive for every \(t\)), and an application of the authors' theory to algebraic coherence. Finally, the authors' theory has the bonus of connections to homological algebra and congruence-class geometries. Unsolved problem (2003): Prove or disprove that \(t\)-regular quasivarieties are \(t\)-deductive.