A Game-Theoretic Unital Classification Theorem for $C^*$-Algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914274358591488 |
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| author | Pi, Jennifer Szachniewicz, Michał Tartarotti, Mira |
| author_facet | Pi, Jennifer Szachniewicz, Michał Tartarotti, Mira |
| contents | We study the complexity of the $KK$-equivalence relation on unital $C^*$-algebras, in the sense of descriptive set theory. We prove that $KK$-equivalence is analytic, which in turn shows that the set of separable $C^*$-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-Fraïssé games (of various lengths) on classifiable $C^*$-algebras and their invariants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01735 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Game-Theoretic Unital Classification Theorem for $C^*$-Algebras Pi, Jennifer Szachniewicz, Michał Tartarotti, Mira Operator Algebras Logic We study the complexity of the $KK$-equivalence relation on unital $C^*$-algebras, in the sense of descriptive set theory. We prove that $KK$-equivalence is analytic, which in turn shows that the set of separable $C^*$-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-Fraïssé games (of various lengths) on classifiable $C^*$-algebras and their invariants. |
| title | A Game-Theoretic Unital Classification Theorem for $C^*$-Algebras |
| topic | Operator Algebras Logic |
| url | https://arxiv.org/abs/2601.01735 |