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- 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

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

Ace Billet Alan Mekler Albin L. Jones Alex Primavesi Alfred Tarski András Hajnal Benoit Mandelbrot Boban Velickovic Chen Meiri Chris Hadfield Ernest Schimmerling Fred Glavin Gabriel Belachsan Hiroshi Sakai Ilijas Farah Itay Neeman Jack Silver Jim Baumgartner John Krueger Judy Roitman Keith Devlin Menachem Magidor Mirna Dzamonja Moti Gitik Murray Bell Paul Erdős Paul Larson Richard Laver Ronald Jensen Saharon Shelah Sakaé Fuchino Stevo Todorcevic Teruyuki Yorioka Wacław Sierpiński

# Tag Archives: sap

## 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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## The failure of diamond on a reflecting stationary set

Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading

## 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