The complexity of being monitorable

Riccardo Camerlo; Francesco Dagnino

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arXiv · 2601.04256

The complexity of being monitorable

Riccardo Camerlo·Francesco Dagnino

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Abstract

We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the family of monitorable sets is $\Pi^0_3$ and determine the exact complexities it can have. In contrast, we show that if $X$ is not second countable then the family of monitorable sets can be much more complex, giving an example where it is $ \Pi^1_1$-complete.

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BibTeX RIS

Riccardo Camerlo, Francesco Dagnino. 2026-01-06. The complexity of being monitorable. https://arxiv.org/abs/2601.04256

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