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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

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

# 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