Free Algebras for Gödel-Löb Provability Logic.

We give a construction of finitely generated free algebras for Godel-Lob provability logic, GL. On the semantic side, this construction yields a notion of canonical graded model for GL and a syntactic definition of those normal forms which are consistent with GL. Our two main techniques are incremental constructions of free algebras and finite duality for partial modal algebras. In order to apply these techniques to GL, we use a rule-based formulation of the logic GL by Avron (which we simplify slightly), and the corresponding semantic characterization that was recently obtained by Bezhanishvili and Ghilardi.