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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

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

# 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