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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

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

# 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