Logic Seminar

Duality theory provides a general framework for strong completeness theorems yielding an exact correspondence between syntax and semantics for various fragments of logic. This talk will survey some known results in this framework, and then present a result relating the Cartesian fragment of ultrametric continuous logic to continuous locally presentable categories. The result treats structures on partial ultrametric spaces, on which predicates may be treated equivalently either as subspaces or as their [0, 1]-valued indicator functions.