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Reading
list:
(A) Model theory:
(1) Bradd's lecture notes:
http://ms.mcmaster.ca/~bradd/courses/math712/
(2) I. Ben Yaacov, A. Berenstein, C. W. Henson, and A.
Usvyatsov,
Model theory for metric structures
http://www.math.uiuc.edu/~henson/cfo/mtfms.pdf
(3) Our paper with David Sherman (although it is #2 in
the series, #1 is actually more advanced and will not be
needed for this project):
http://www.math.yorku.ca/~ifarah/Ftp/2010d-stable-th.pdf
(Note: Chang-Keisler's book `Continuous model theory' is
dated and not quite what we will need.)
(B) Functional analysis:
There is a number of excellent books in the subject. Among
them are:
Pedersen, Gert Kjærgård. Analysis now.
Vol. 2. Springer, 1995.
Conway, John B. A course in functional analysis.
Vol. 96. Springer, 1990.
Rudin, Walter. Functional analysis. International series
in pure and applied mathematics. McGraw-Hill (1991).
Zimmer, Robert J. Essential results of functional analysis.
University of Chicago Press, 1990.
Each of these books contains way more material than we
can possibly cover in two months. Central topics from the
functional analysis that we will need are the following:
Hilbert spaces, operators on Hilbert spaces, spectral theorem,
continuous functional calculus.
(C) C*-algebras.
(1) An introduction is given in Ilijas's Singapore lecture
notes:
http://www.math.yorku.ca/~ifarah/Ftp/2012g08-singapore-notes-final.pdf
There are many excellent books on C*-algebras (some of
them published by the Fields Institute) but the above will
do for now.
(D) Further reading.
(1) Last year's project is presented here
http://www.math.yorku.ca/~ifarah/Ftp/types-23dec12.pdf
(2) Slides from Ilijas's Logic Colloquium 2012 lectures
also contain some information on the `big picture' (lecture
three is most relevant to our project). Attached here:
Lecture
1
Lecture 2
Lecture 3
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