Geodesic
Elementary equivalence and disintegration of tracial von Neumann algebras
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e105

Voir la notice de l'article provenant de la source Cambridge University Press

We prove an analog of the disintegration theorem for tracial von Neumann algebras in the setting of elementary equivalence rather than isomorphism, showing that elementary equivalence of two direct integrals of tracial factors implies fiberwise elementary equivalence under mild, and necessary, hypotheses. This verifies a conjecture of Farah and Ghasemi. Our argument uses a continuous analog of ultraproducts where an ultrafilter on a discrete index set is replaced by a character on a commutative von Neumann algebra, which is closely related to Keisler randomizations of metric structures. We extend several essential results on ultraproducts, such as Łoś’s theorem and countable saturation, to this more general setting. 
Gao, David; Jekel, David. Elementary equivalence and disintegration of tracial von Neumann algebras. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e105. doi: 10.1017/fms.2025.10066
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