David Sherman
Model theory of operator algebras II: Model theory.
Wed, 04/07/2010 - 15:01 — SomNambulAuthors: Ilijas Farah, Bradd Hart, David Sherman
Subjects: Logic
AbstractWe introduce a version of logic for metric structures suitable for
applications to C*-algebras and tracial von Neumann algebras. We also prove a
purely model-theoretic result to the effect that the theory of a metric
structure is stable if and only if all of its ultrapowers associated with
nonprincipal ultrafilters on N are isomorphic even when the Continuum
Hypothesis fails.On cardinal invariants and generators for von Neumann algebras.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: David Sherman
Subjects: Operator Algebras
AbstractWe demonstrate how virtually all common cardinal invariants associated to a
von Neumann algebra M can be computed from the decomposability number, dec(M),
and the minimal cardinality of a generating set, gen(M).Model theory of operator algebras I: Stability.
Thu, 08/20/2009 - 23:06 — SomNambulAuthors: Ilijas Farah, Bradd Hart, David Sherman
Subjects: Operator Algebras
AbstractSeveral authors have considered whether the ultrapower and the relative
commutant of a C*-algebra or II_1 factor depend on the choice of the
ultrafilter. We show that the negative answer to each of these questions is
equivalent to the Continuum Hypothesis, extending results of Ge-Hadwin and the
first author.
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