September 9, 2006

Carnegie Mellon University

Background reading

• 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
    Jech, Thomas, Set theory, Springer Monographs in Mathematics, 2003, ISBN 3-540-44085-2
• Less important for the workshop but worth reviewing in Jech's textbook 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
    Kanamori, Akihiro, The higher infinite, Springer Monographs in Mathematics, 2003, ISBN 3-540-00384-3

• 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 0-8218-3604-8
  • 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