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- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013

### Keywords

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

# 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