The Assertional Logics of Pointed Fixedpoint Discriminator Varieties
by
Matthew Spinks
Coauthors: Robert Bignall

Using the framework of algebraisable logics developed by Blok and Pigozzi, we investigate the connections between the assertional logics of pointed fixedpoint discriminator varieties, and the assertional logic of the variety of implicative BCSK-algebras. The variety of implicative BCSK-algebras is a non-commutative generalisation of Abbott's variety of implication algebras; its assertional logic is closely related to the purely implicational fragment of the classical propositional calculs. The main results of the talk are the following:

1. The assertional logic of the variety of implicative BCSK-algebras is formulawise definitionally equivalent to the assertional logic of the pure pointed fixedpoint discriminator variety.

2. The assertional logic of the variety of implicative BCSK-algebras is formulawise definitionally equivalent to the least algebraisable implicational fragment of the assertional logic of the pure pointed discriminator variety.

3. A strongly algebraisable deductive system is classically algebraisable iff it is formulawise definitionally equivalent to a definitional expansion of an axiomatic extension of the assertional logic of the variety of implicative BCSK-algebras, possibly with additional compatible logical operations.

Date received: September 12, 2003