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### Recent blog posts

- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- 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

### Keywords

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

# 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
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## 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