### 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

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

# 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