Omitting types and AF algebras
Kevin Carlson, Enoch Cheung, Ilijas Farah, Alexander Gerhardt-Bourke,, Bradd Hart, Leanne Mezuman, Nigel Sequeira, Alexander Sherman
TL;DR
This paper provides a model-theoretic framework to characterize UHF and AF algebras as C*-algebras that omit specific types, offering new insights into their structural properties.
Contribution
It introduces a novel model-theoretic approach to characterize UHF and AF algebras by their omission of certain types, bridging operator algebras and logic.
Findings
UHF algebras characterized by type omission
AF algebras characterized by type omission
Model-theoretic criteria for classifying C*-algebras
Abstract
We give model-theoretic characterizations of UHF algebras and of AF algebras as C*-algebras that omit certain sets of types.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models