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

# Tag Archives: Generalized Clubs

## 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

## On guessing generalized clubs at the successors of regulars

Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading