Publisher's 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 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 Ôêù - 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*-algebras sense)
