# The Topological Mu-Calculus: completeness and decidability

arXiv: https://arxiv.org/abs/2105.08231 · HTML: https://mlsanity.com/paper/2105.08231/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2021.

## Built on by (most cited first, 1 of 1)

- [Common Knowledge Always, Forever](https://mlsanity.com/paper/2602.13914/) (2026)

## Abstract (arXiv)

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 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.