 
Summary: SET THEORY AND OPERATOR ALGEBRAS
ILIJAS FARAH AND ERIC WOFSEY
These notes are based on the sixhour Appalachian Set Theory workshop
given by Ilijas Farah on February 9th, 2008 at Carnegie Mellon Univer
sity. The first half of the workshop (Sections 13) consisted of a review of
Hilbert space theory and an introduction to Calgebras, and the second half
(Sections 46) outlined a few settheoretic problems relating to Calgebras.
The number and variety of topics covered in the workshop was unfortunately
limited by the available time.
Good general references on Hilbert spaces and Calgebras include [8],
[10], [14], [27], and [35]. An introduction to spectral theory is given in [9].
Most of the omitted proofs can be found in most of these references. For a
survey of applications of set theory to operator algebras, see [36].
Acknowledgments. We would like to thank Nik Weaver for giving us a
kind permission to include some of his unpublished results. I.F. would like to
thank George Elliott, N. Christopher Phillips, Efren Ruiz, Juris Stepr¯ans,
Nik Weaver and the second author for many conversations related to the
topics presented here. I.F. is partially supported by NSERC.
Contents
1. Hilbert spaces and operators 2
