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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

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