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010 a| 2022007684;

020 a| 9781470447571q| (paperback);

020 z| 9781470466268q| (epub);

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100 1 a| Farah, Ilijas,d| 1966-=| ^A466241;

245 10 a| Model theory of C-algebrash| [electronic resource] /c| Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter.;

260 a| Providence :b| American Mathematical Society,c| 2021.;

300 a| viii, 127 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 271, number 1324 (first of 7 numbers);

504 a| Includes bibliographical references and index.;

506 a| Available only to authorized users.;

520 a| "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 across all 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-algebras with 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 divisibility 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| C*-algebras.=| ^A81867;

650 0 a| Model theory.=| ^A21581;

650 7 a| Functional analysis -- Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) -- General theory of $C$-algebras.2| msc;

650 7 a| Functional analysis -- Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) -- Classifications of $C*$-algebras.2| msc;

650 7 a| Mathematical logic and foundations -- Model theory -- Ultraproducts and related constructions.2| msc;

650 7 a| Mathematical logic and foundations -- Model theory -- Applications of model theory.2| msc;

650 7 a| Mathematical logic and foundations -- Set theory -- Descriptive set theory.2| msc;

650 7 a| Mathematical logic and foundations -- Model theory -- Model-theoretic forcing.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6715039;

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Model theory of C-algebras / Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter.

Author/creator	Farah, Ilijas, 1966-
Format	Electronic
Publication Info	Providence : American Mathematical Society, 2021.
Description	viii, 127 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	C*-algebras. Model theory.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 271, number 1324 (first of 7 numbers)
Abstract	"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 across all 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-algebras with 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 divisibility 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"-- Provided by publisher.
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007684
ISBN	9781470447571 (paperback)
ISBN	(epub)

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Model theory of C-algebras / Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter.

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