Appalachian set theory
September 9, 2006
Carnegie Mellon University
- Generic ultrapowers by normal ideals over ω1
are central to the workshop.
Those unfamiliar with these can read about them on
pages 420-423 of
Springer Monographs in Mathematics, 2003, ISBN 3-540-44085-2
- Less important for the workshop but worth reviewing in
are the sections on precipitous ideals (pages 424-426)
and precipitousness of the nonstationary ideal (pages 445-450)
but only as they apply to ideals on ω1.
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 99-111 of
The higher infinite,
Springer Monographs in Mathematics, 2003,
- 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,
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. 71-125