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On constructing free algebras and properties of free Heyting algebras

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If you have a question about this talk, please contact Julia Goedecke.

(joint work with Sam van Gool)

In this talk we give a general method for constructing free algebras, based on partial algebras. We show that, for certain varieties V, the finitely generated free V algebras may be described as the colimit of a chain of partial algebras that is obtained by repeated application of a functor. We give sufficient conditions on V for our method to apply and use duality theory to show that our method applies in particular to certain classes of modal algebras.

In the second part of the talk we focus on Heyting algebras. N. Bezhanishvilli and M. Gehrke have given a description of finitely generated free Heyting algebras as a colimit of finite algebras. We discuss some current research that uses this description to study properties of free Heyting algebras. In particular, we relate this construction to the universal model in intuitionistic logic.

This talk is part of the Category Theory Seminar series.

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