### Archives

### Recent blog posts

- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013

### Keywords

Diamond Singular Density polarized partition relation diamond star Mandelbrot set Large Cardinals Non-saturation Erdos-Hajnal graphs Shelah's Strong Hypothesis Minimal Walks S-Space Poset Absoluteness Forcing Whitehead Problem Axiom R Martin's Axiom Club Guessing Antichain incompactness Ostaszewski square Universal Sequences Forcing Axioms Cardinal Invariants Rado's conjecture Prevalent singular cardinals Almost-disjoint famiy Successor of Regular Cardinal Knaster very good scale stationary reflection Hedetniemi's conjecture Singular Cofinality OCA Kurepa Hypothesis Rock n' Roll approachability ideal reflection principles Hereditarily Lindelöf space L-space PFA Almost countably chromatic b-scale ccc P-Ideal Dichotomy Chromatic number PFA(S)[S] Partition Relations Cohen real Dushnik-Miller Generalized Clubs free Boolean algebra Square-Brackets Partition Relations stationary hitting Uniformization Foundations tensor product graph Aronszajn tree weak square Rainbow sets middle diamond Souslin Tree Small forcing Erdos Cardinal Weakly compact cardinal Sakurai's Bell inequality Constructible Universe Prikry-type forcing projective Boolean algebra Cardinal function sap square weak diamond Successor of Singular Cardinal Singular cardinals combinatorics

# Tag Archives: stationary hitting

## 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 … Continue reading

Posted in Open Problems, Publications
Tagged 03E05, 03E35, 03E50, approachability ideal, Club Guessing, Diamond, diamond star, Non-saturation, sap, Souslin Tree, square, stationary hitting, Uniformization, Whitehead Problem
2 Comments

## A relative of the approachability ideal, diamond and non-saturation

Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading