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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

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

# 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