The topological mu-calculus: completeness and decidability
Alexandru Baltag, Nick Bezhanishvili, David Fernandez Duque
Abstract:
We study the topological mu-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over T0 and TD spaces. We also investigate relational
mu-calculus, providing general completeness results for all natural fragments of mu-calculus over many different classes of relational frames. Unlike most other such proofs for
mu-calculus, ours is model-theoretic, 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.