Dualities of various types have been used by different authors to
describe free and projective objects in a large
number of classes of algebras. Particularly, natural dualities provide a
general tool to describe free objects. In
this talk we present two interesting applications of this fact.
We first provide a combinatorial classification of unification problems
by their unification type for the
varieties of Bounded Distributive Lattices, Kleene algebras, De Morgan
algebras. Finally we provide axiomatizations forsingle
and multiple conclusion admissible rules for the varieties of Kleene
algebras, De Morgan algebras, Stone algebras.
- Analytic Topology in Mathematics and Computer Science