Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras
| Autor: | Farah, Ilijas, Jekel, David, Pi, Jennifer |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neumann algebra $\mathcal{N}$ is never model complete if its direct integral decomposition contains $\mathrm{II}_1$ factors $\mathcal{M}$ such that $M_2(\mathcal{M})$ embeds into an ultrapower of $\mathcal{M}$. The proof in the case of $\mathrm{II}_1$ factors uses an explicit construction based on random matrices and quantum expanders. Comment: 38 pages, comments are welcome |
| Databáze: | arXiv |
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