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These notes are based on the six-hour Appalachian Set Theory workshop given by Ilijas Farah on February 9th, 2008 at Carnegie Mellon University. The first half of the workshop (Sections 1-3) consisted of a review of Hilbert space theory and an introduction to C *-algebras, and the second half (Sections 4–6) outlined a few set-theoretic problems relating to(More)
In this paper we extend the classification results obtained by Rørdam in the paper [15]. We prove a strong classification theorem for the unital essential extensions of Kirchberg algebras, a classification theorem for the non-stable, non-unital essential extensions of Kirchberg algebras, and we characterize the range in both cases. The invariants are cyclic(More)
Semigroup C*-algebras for right-angled Artin monoids were introduced and studied by Crisp and Laca. In the paper at hand, we are able to present the complete answer to their question of when such C*-algebras are isomorphic. The answer to this question is presented both in terms of properties of the graph defining the Artin monoids as well as in terms of(More)
We classify real Kirchberg algebras using united K-theory. Precisely, let A and B be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that A C and B C are also simple. In the stable case, A and B are iso-morphic if and only if K CRT (A) ∼ = K CRT (B). In the unital case, A and B are isomorphic if(More)
The original version of this note was based on two talks given by Efren Ruiz at the Toronto Set Theory seminar in November 2005. This very tentative note and my Luminy talk form an attempt to record the ideas from these talks and draw more attention of set theorists to Naimark's problem (Problem 5.1 below). An excellent invitation to C*-algebras for(More)