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### Recent blog posts

- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

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

# 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