### Archives

### 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

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

# 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