A Game-Theoretic Unital Classification Theorem for $C^*$-Algebras
Operator Algebras
2026-01-26 v2 Logic
Abstract
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 shows that the set of separable -algebras satisfying the UCT is analytic. This allows us to prove a game-theoretic refinement of the unital classification theorem: there is a transfer of strategies between Ehrenfeucht-Fra\"iss\'e games (of various lengths) on classifiable -algebras and their invariants.
Keywords
Cite
@article{arxiv.2601.01735,
title = {A Game-Theoretic Unital Classification Theorem for $C^*$-Algebras},
author = {Jennifer Pi and Michał Szachniewicz and Mira Tartarotti},
journal= {arXiv preprint arXiv:2601.01735},
year = {2026}
}
Comments
46 pages. Submitted version