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- 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

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

# 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