Jensen’s diamond principle and its relatives

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127).

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:

  1. Diamond
  2. Weak Diamond and the Uniformization Property
  3. The Souslin Hypothesis and Club Guessing
  4. Saturation of the Nonstationary Ideal
  5. Index
  6. References

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Citation information:

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.

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2 Responses to Jensen’s diamond principle and its relatives

  1. saf says:

    Update: David Aspero announced a negative answer to Question 13 from our list. The title of his paper is “The consistency of a club-guessing failure at the successor of a regular cardinal”.

       0 likes

  2. saf says:

    In her Oberwolfach talk, Heike Mildenberger just announced a negative answer to Question 17! This is joint work with Shelah (the paper # is 988).

       1 likes

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