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Preservation of
elementarity by tensor products of tracial von Neumann
algebras
Ilijas Farah and Saeed Ghasemi |
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Vol. 332 (2024), No. 1, 91–113
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DOI: 10.2140/pjm.2024.332.91
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Abstract |
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Tensoring with type I algebras preserves elementary equivalence in the category of tracial von Neumann algebras. The proof involves a novel and general Feferman–Vaught-type theorem for direct integrals of metric structures. |
Keywords
type $\mathrm{II}_1$ von Neumann algebras, direct
integrals, preservation of elementarity, Feferman–Vaught
theorem, continuous logic
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Mathematical Subject Classification
Primary: 03C66, 03C98, 46L10
Secondary: 46L54
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Milestones
Received: 17 April 2023
Revised: 5 September 2024
Accepted: 18 October 2024
Published: 20 November 2024
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Authors |
| Ilijas Farah | |
| Department of Mathematics and
Statistics York University North York, ON Canada |
Matematički Institut SANU Beograd Serbia |
| Saeed Ghasemi | |
| Department of Mathematics and
Statistics York University North York, ON Canada |
Department of Mathematical
Sciences Lakehead University Thunder Bay, ON Canada |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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