The complexity of being monitorable
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914239297355776 |
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| author | Camerlo, Riccardo Dagnino, Francesco |
| author_facet | Camerlo, Riccardo Dagnino, Francesco |
| contents | 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 $Π^0_3$ 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 $ Π^1_1$-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04256 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The complexity of being monitorable Camerlo, Riccardo Dagnino, Francesco Logic Logic in Computer Science 03B70, 03E15, 68Q60 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 $Π^0_3$ 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 $ Π^1_1$-complete. |
| title | The complexity of being monitorable |
| topic | Logic Logic in Computer Science 03B70, 03E15, 68Q60 |
| url | https://arxiv.org/abs/2601.04256 |