Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club guessing, and anti-diamond principles such as uniformization.
A collection of open problems is included.
Table of Contents:
- Weak Diamond and the Uniformization Property
- The Souslin Hypothesis and Club Guessing
- Saturation of the Nonstationary Ideal
A. Rinot, Jensen’s diamond principle and its relatives, Set Theory and Its Applications, Contemp. Math., 533: 125-156, Amer. Math. Soc., Providence, RI, 2011.