### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- 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

### Keywords

Singular coﬁnality Hereditarily Lindelöf space 11P99 Fat stationary set Fodor-type reflection PFA Ostaszewski square Dushnik-Miller Rock n' Roll ccc Erdos-Hajnal graphs stationary hitting free Boolean algebra Shelah's Strong Hypothesis Almost-disjoint famiy Reduced Power Commutative cancellative semigroups weak diamond Kurepa Hypothesis Whitehead Problem HOD Poset approachability ideal Sakurai's Bell inequality S-Space Aronszajn tree Parameterized proxy principle xbox Chromatic number Cardinal function OCA sap Stevo Todorcevic Prikry-type forcing Generalized Clubs Successor of Regular Cardinal tensor product graph Coherent tree stationary reflection Erdos Cardinal 20M14 reflection principles square Rainbow sets Partition Relations Slim tree Minimal Walks Prevalent singular cardinals Weakly compact cardinal P-Ideal Dichotomy Singular Density Souslin Tree Constructible Universe Axiom R Mandelbrot set projective Boolean algebra Almost Souslin weak square Singular Cofinality Diamond Jonsson cardinal Selective Ultrafilter Forcing Singular cardinals combinatorics Hedetniemi's conjecture L-space 05D10 polarized partition relation Club Guessing b-scale Chang's conjecture PFA(S)[S] Antichain Ascent Path Almost countably chromatic Microscopic Approach Hindman's Theorem Successor of Singular Cardinal diamond star Absoluteness middle diamond Knaster incompactness coloring number Uniformization Square-Brackets Partition Relations Forcing Axioms Cohen real Martin's Axiom Universal Sequences Cardinal Invariants 05A17 Fast club Small forcing very good scale Non-saturation Foundations Rado's conjecture Large Cardinals

# 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