Appalachian set theory
September 9, 2006
Carnegie Mellon University
Background reading
 Generic ultrapowers by normal ideals over ω_{1}
are central to the workshop.
Those unfamiliar with these can read about them on

pages 420423 of
Jech, Thomas,
Set theory,
Springer Monographs in Mathematics, 2003, ISBN 3540440852
 Less important for the workshop but worth reviewing in
Jech's textbook
are the sections on precipitous ideals (pages 424426)
and precipitousness of the nonstationary ideal (pages 445450)
but only as they apply to ideals on ω_{1}.

The use of sharps will be avoided to the extent possible but they will
arise at least once. The relevant background material is on

pages 99111 of
Kanamori, Akihiro,
The higher infinite,
Springer Monographs in Mathematics, 2003,
ISBN 3540003843
 Towers of measures and weakly homogeneous trees will come up
during the workshop. A few basic facts about these will be listed and
used in black box fashion. The proofs do not take long to present but
with time limited, something must be omitted.
The following are sources for the relevant facts,
their proofs and much more.

Sections 1.2 and 1.3 of
Larson, Paul B., The stationary tower,
University Lecture Series 32, Amer. Math. Soc., 2004,
ISBN 0821836048

Kanamori, see above

Section 2 of
Martin, Donald A. and Steel, John R.,
A proof of projective determinacy,
J. Amer. Math. Soc., vol. 2, 1989, no. 1, pp. 71125