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 with a Discrete Group Action
Alexander Berenstein, Juan Manuel Pérez
In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory…
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…