Isomorphism of almost locally compact Polish metric structures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912532358234112 |
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| author | Malicki, Maciej |
| author_facet | Malicki, Maciej |
| contents | A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always classifiable by countable structures. This allows to remove a gap in the proof presented in \cite{Ma} of a positive answer to a question of Gao and Kechris, who asked whether isometry of locally compact Polish metric spaces is classifiable by countable structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphism of almost locally compact Polish metric structures Malicki, Maciej Logic 03E15, 03C66, 03C75 A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always classifiable by countable structures. This allows to remove a gap in the proof presented in \cite{Ma} of a positive answer to a question of Gao and Kechris, who asked whether isometry of locally compact Polish metric spaces is classifiable by countable structures. |
| title | Isomorphism of almost locally compact Polish metric structures |
| topic | Logic 03E15, 03C66, 03C75 |
| url | https://arxiv.org/abs/2508.07765 |