5 papers · 1 filter
Free Independence is not definable
William Boulanger, Jakub Curda, Emma Harvey +2
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 captur…
A Game-Theoretic Unital Classification Theorem for -Algebras
Jennifer Pi, MichaÅ Szachniewicz, Mira Tartarotti
We study the complexity of the -equivalence relation on unital -algebras, in the sense of descriptive set theory. We prove that -equivalence is analytic, which in turn…
Strong convergence to operator-valued semicirculars
David Jekel, Yoonkyeong Lee, Brent Nelson +1
We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $η= (η_{i,j}…
Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras
Ilijas Farah, David Jekel, Jennifer Pi
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 Neuman…
Embeddings into the ultrapower of the Jiang-Su algebra
Ben Bouwen, Jennifer Pi
We study existence of embeddings into ultrapowers of the Jiang-Su algebra and the Razak-Jacelon algebra . More specifically, we show that the cone over a…