Sahlqvist preservation for topological fixed-point logic
Nick Bezhanishvili, Sumit Sourabh
Abstract:
We introduce a new order-topological semantics for the positive modal mu-calculus over modal compact Hausdorff spaces, which are generalizations of descriptive frames. We define Sahlqvist sequents in this language and prove Esakia's lemma and Sahlqvist preservation theorem in this semantics. We show that every Sahlqvist sequent has a frame correspondent in first-order logic with fixed-point operators.
Keywords: Modal mu-calculus, order-topological semantics, Sahlqvist correspondence, canonicity