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### Recent blog posts

- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- 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

### Keywords

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

# 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