(Joint work with John Harding)
Recently Ciabattoni, Galatos, and Terui have introduced a new notion of completion of residuated lattices which they call the hyperMacNeille completion. This type of completion plays a central role in their work on establishing the admissibility of the cutrule in certain types of hypersequent calculi for substructural logics. In this talk we will focus on describing the hyperMacNeille completion of Heyting algebras. We show that the hyperMacNeille completion and the MacNeille completion coincide for socalled centrally supplemented Heyting algebras. That is, Heyting algebras with orderduals being Stone lattices. In fact, we show that any Heyting algebra A has a centrally supplemented extension S(A) such that the hyperMacNeille completion of A is isomorphic to the MacNeille completion of S(A). These centrally supplemented extensions turn out to be the orderduals of the 1Stone extensions originally introduced by Davey in 1972.
