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### Recent blog posts

- 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

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

# 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