3 papers
math.LO2025
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.…
math.LO2025
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…
math.LO2025
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 the…