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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

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

# 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