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Logic and C*-Algebras: Set Theoretical Dichotomies in the Theory of Continuous Quotients

Logic and C*-Algebras: Set Theoretical Dichotomies in the Theory of Continuous Quotients

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Title: Logic and C*-Algebras: Set Theoretical Dichotomies in the Theory of Continuous Quotients
Author: Vignati, Alessandro
Abstract: Given a nonunital C*-algebra A one constructs its corona algebra M(A)/A. This is the noncommutative analog of the Cech-Stone remainder of a topological space. We analyze the two faces of these algebras: the first one is given assuming CH, and the other one arises when Forcing Axioms are assumed. In their first face, corona C*-algebras have a large group of automorphisms that includes nondefinable ones. The second face is the Forcing Axiom one; here the automorphism group of a corona C*-algebra is as rigid as possible, including only definable elements.
Subject: Logic
Keywords: C*-algebras
Set theory
Forcing axioms
Type: Electronic Thesis or Dissertation
Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
URI: http://hdl.handle.net/10315/34266
Supervisor: Farah, Ilijas
Degree: PhD - Doctor of Philosophy
Program: Mathematics & Statistics
Exam date: 2017-04-21
Publish on: 2018-03-01

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