Canonical extensions in the setting of lattice-based algebras
by
Hilary Priestley
Mathematical Institute, University of Oxford
Coauthors: Brian Davey & Mai Gehrke

For a finitely generated lattice-based variety V, the canonical extension of an algebra in V coincides with its profinite completion (a recent result of John Harding). We shall indicate how the existence of a natural duality for V yields an alternative description of the profinite completion, alias canonical extension, of any A ∈ V. This approach provides new insights into how canonicity of V comes about, how canonical extensions behave in the finitely generated case, and how topological ideas can be exploited. In addition, the natural duality supplies a new form of complete relational semantics.

Date received: June 11, 2007