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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

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

# 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