ON EVERYWHERE STRONGLY LOGIFIABLE ALGEBRAS
Tommaso Moraschini · 2015
In the late 80’s Blok and Pigozzi provided a uniform framework for the al-gebraic approach to the analysis of propositional logics, namely the theory of algebraizability [1]. In general the equivalent algebraic semantics Alg∗L of an algebraizable logic L is a generalized quasi-variety. However, most of the well-known algebraizable logics have an equivalent algebraic semantics that is a vari-ety. This posed the natural question, sometimes called in the literature “variety problem”, of explaining this phenomenon by finding some meaningful sufficient conditions under which the equivalent algebraic semantics of an algebraizable logic is a variety: conditions of this kind have been obtained for example in [2,3,6,7,8]. Following [1] a logic L is called strongly algebraizable if it is alge-braizable and Alg∗L is a variety. The starting point of this talk is the attempt to define what does it mean that a finite (non-trivial) algebra A behaves in the best possible way from the point of view of Blok and Pigozzi’s algebraizability theory. Obviously, several definitions can be proposed to formalize this non-mathematical concept. Our