Luca Carai (Università di Milano) will give a talk on
Free algebras and coproducts in varieties of Gödel algebras
Abstract:
Free algebras in varieties of Heyting algebras play an important role in the study of superintuitionistic logics as they are, up to isomorphism, Lindenbaum-Tarski algebras. Gödel algebras, which are the Heyting algebras satisfying the prelinearity axiom (x→y)∨(y→x)=1, provide the algebraic semantics for the propositional superintuitionistic logic known as the Gödel-Dummett logic.
In this talk we will see how to utilize Priestley and Esakia dualities to dually describe free algebras and coproducts in all varieties of Gödel algebras. This method yields tangible dual descriptions that generalize known results for the finitely generated case, allowing us to establish both a formula for computing the depth of coproducts of Gödel algebras and a proof that all free Gödel algebras are bi-Heyting algebras. I will conclude by mentioning some ongoing projects that aim to obtain similar dual descriptions of free algebras in varieties of algebraic structures related to Gödel algebras.