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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)
It is said that the vorticity of a congruence plays the role of rate of rotation for the precession of a gyroscope moving along a world-line belonging to the congruence. Our aim is to determine the evolution equation for the angular momentum of a gyrosocope with respect to an arbitrary time-like congruence, i.e, a reference congruence which does not contain(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 problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate(More)