Free Independence is not definable
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_ | 1866912922196770816 |
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| author | Boulanger, William Curda, Jakub Harvey, Emma Li, Yizhi Pi, Jennifer |
| author_facet | Boulanger, William Curda, Jakub Harvey, Emma Li, Yizhi Pi, Jennifer |
| contents | Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a definable set. We prove that pairs of freely independent elements do not form a definable set in the sense of continuous model theory, relative to the theory of both C$^*$-probability spaces and tracial von Neumann algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free Independence is not definable Boulanger, William Curda, Jakub Harvey, Emma Li, Yizhi Pi, Jennifer Operator Algebras Logic Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a definable set. We prove that pairs of freely independent elements do not form a definable set in the sense of continuous model theory, relative to the theory of both C$^*$-probability spaces and tracial von Neumann algebras. |
| title | Free Independence is not definable |
| topic | Operator Algebras Logic |
| url | https://arxiv.org/abs/2510.04836 |