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### Recent blog posts

- 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

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

# 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