A non-computable c.e. closed subset of $[0,1]$
Logic
2025-08-11 v1
Abstract
We prove that there exists a closed subset of that is not homeomorphic to any computably compact space. We show that the index set of c.e. subspaces of that admit a computably compact presentation is not arithmetical, as witnessed by subsets of . The index set result is new for computable Polish spaces in general, not only for those realised as c.e. closed subsets of .
Keywords
Cite
@article{arxiv.2508.06187,
title = {A non-computable c.e. closed subset of $[0,1]$},
author = {Serikzhan Badaev and Nikolay Bazhenov and Sergey Goncharov and Birzhan Kalmurzayev and Alexander Melnikov},
journal= {arXiv preprint arXiv:2508.06187},
year = {2025}
}
Comments
19 pages, accepted to Journal of Logic and Computation