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### Recent blog posts

- 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

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

# 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