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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

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

# 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