The Topological Mu-Calculus: completeness and decidability - Baltag, Alexandru; Bezhanishvili, Nick; Fernandez-Duque, David (Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, 2021)
We study the topological µ-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over T 0 and T D spaces. We also investigate relational µ-calculus, providing general completeness results for all natural fragments of µ-calculus over many different classes of relational frames. Unlike most other such proofs for µ-calculus, ours is modeltheoretic, making an innovative use of a known Modal Logic method (-the 'final' submodel of the canonical model), that has the twin advantages of great generality and essential simplicity.