Model Theory of Mathrm C-algebras - Couverture souple

Farah, Ilijas; Hart, Bradd; Lupini, Martino; Robert, Leonel; Tikuisis, Aaron

Couverture souple

ISBN 10 : 1470447576 ISBN 13 : 9781470447571

Editeur : American Mathematical Society, 2021

Synopsis

"A number of significant properties of C-algebras can be expressed in continuous logic, or at least in terms of definable (in a model-theoretic sense) sets. Certain sets, such as the set of projections or the unitary group, are uniformly definable acrossall C-algebras. On the other hand, the definability of some other sets, such as the connected component of the identity in the unitary group of a unital C- algebra, or the set of elements that are Cuntz-Pedersen equivalent to 0, depends on structural properties of the C-algebra in question. Regularity properties required in the Elliott programme for classification of nuclear C-algebras imply the definability of some of these sets. In fact any known pair of separable, nuclear, unital and simple C-algebraswith the same Elliott invariant can be distinguished by their first-order theory. Although parts of the Elliott invariant of a classifiable (in the technical C-algebraic sense) C-algebra can be reconstructed from its model-theoretic imaginaries, the information provided by the theory is largely complementary to the information provided by the Elliott invariant. We prove that all standard invariants employed to verify non-isomorphism of pairs of C-algebras indistinguishable by their K-theoretic invariants(the diibility properties of the Cuntz semigroup, the radius of comparison, and the existence of finite or infinite projections) are invariants of the theory of a C-algebra"--

A propos du livre

À propos de l'auteur

Ilijas Farah, York University, Toronto, Ontario, Canada.

Bradd Hart, McMaster University, Hamilton, Ontario, Canada.

Martino Lupini, Victoria University of Wellington, Canada.

Leonel Robert, University of Louisiana at Lafayette, LA.

Aaron Tikuisis, University of Ottawa, Ontario, Canada.

Alessandro Vignati, York University, Toronto, Ontario, Canada.

Wilhelm Winter, University of Munster, Einsteinstrasse, Munster.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2021
• Langue: anglais
• ISBN 10: 1470447576
• ISBN 13: 9781470447571
• Reliure: Broché
• Nombre de pages: 127
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible