Borel completeness of Tits buildings with no rank 3 residues of spherical type
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912742117474304 |
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| author | Paolini, Gianluca Quadrellaro, Davide Emilio |
| author_facet | Paolini, Gianluca Quadrellaro, Davide Emilio |
| contents | We prove that, for every Coxeter diagram $D$ with no rank $3$ residues of spherical type and such that $D$ has not only edges labelled by $2$, the space of countable (Tits) buildings of type $D$ is Borel complete, that is, classifying countable buildings of type $D$ up to isomorphism is as hard as classifying countable graphs up to isomorphism. In particular, for every $n\geq 3$, the space of countable generalised $n$-gons is Borel complete. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_17630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borel completeness of Tits buildings with no rank 3 residues of spherical type Paolini, Gianluca Quadrellaro, Davide Emilio Logic Combinatorics 03E15, 20E42, 51E12, 51E24 We prove that, for every Coxeter diagram $D$ with no rank $3$ residues of spherical type and such that $D$ has not only edges labelled by $2$, the space of countable (Tits) buildings of type $D$ is Borel complete, that is, classifying countable buildings of type $D$ up to isomorphism is as hard as classifying countable graphs up to isomorphism. In particular, for every $n\geq 3$, the space of countable generalised $n$-gons is Borel complete. |
| title | Borel completeness of Tits buildings with no rank 3 residues of spherical type |
| topic | Logic Combinatorics 03E15, 20E42, 51E12, 51E24 |
| url | https://arxiv.org/abs/2510.17630 |