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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

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

# 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