10 papers
Non-computability of -theory for computably presented C*-algebras
Christopher J. Eagle, Isaac Goldbring, Timothy H. McNicholl +1
We give an example of a unital C*-algebra with a computable presentation and for which neither nor has a computable presentation.
Computable -theory for C*-algebras II: AF algebras
Christopher J. Eagle, Isaac Goldbring, Timothy H. McNicholl
We continue the study of the effective content of -theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to…
General real-valued theories with the Schröder-Bernstein property are stable
Alexander Berenstein, Nicolás Cuervo Ovalle, Isaac Goldbring
We show that every general theory à la Keisler with the Schröder-Bernstein property is stable. This generalizes the corresponding result from classical logic due to John Goodrick.…
On definability of C*-tensor norms
Isaac Goldbring, Thomas Sinclair
We initiate the study of definability (in the model-theoretic sense) of C*-tensor norms. We show that neither the minimal nor maximal tensor norms are definable uniformly over all…
The Schröder-Bernstein property for operators on Hilbert spaces
Nicolás Cuervo Ovalle, Isaac Goldbring, Netanel Levi
We establish that the complete theory of a Hilbert space equipped with a normal operator has the Schröder-Bernstein property. This answers a question of Argoty, Berenstein, and th…
Model theory of Hilbert spaces expanded by normal operators
Alexander Berenstein, Nicolás Cuervo Ovalle, Isaac Goldbring
We study expansions of Hilbert spaces with a bounded normal operator . We axiomatize this theory in a natural language and identify all of its completions. We prove the definabi…