A. Baltag, N. Bezhanishvili, David Fern'andez-Duque
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The Topological Mu-Calculus: completeness and decidability
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 T0 and TD 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.
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