Probably isomorphic structures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915368969175040 |
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| author | Farah, Ilijas Vaccaro, Andrea |
| author_facet | Farah, Ilijas Vaccaro, Andrea |
| contents | Two structures $M, N$ in the same language are called probably isomorphic if they (or, in case of metric structures, their completions) are isomorphic after forcing with the Lebesgue measure algebra. We show that, if $M$ and $N$ are discrete structures, or extremal models of a non-degenerate simplicial theory, then $M$ and $N$ are probably isomorphic if and only if $L^1([0,1], M) \cong L^1([0,1], N)$. We moreover employ some of the set-theoretic arguments used to prove the aforementioned result to characterize when nontrivial ultraproducts of diffuse von Neumann algebras are tensorially prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probably isomorphic structures Farah, Ilijas Vaccaro, Andrea Logic Operator Algebras Two structures $M, N$ in the same language are called probably isomorphic if they (or, in case of metric structures, their completions) are isomorphic after forcing with the Lebesgue measure algebra. We show that, if $M$ and $N$ are discrete structures, or extremal models of a non-degenerate simplicial theory, then $M$ and $N$ are probably isomorphic if and only if $L^1([0,1], M) \cong L^1([0,1], N)$. We moreover employ some of the set-theoretic arguments used to prove the aforementioned result to characterize when nontrivial ultraproducts of diffuse von Neumann algebras are tensorially prime. |
| title | Probably isomorphic structures |
| topic | Logic Operator Algebras |
| url | https://arxiv.org/abs/2507.01518 |