### 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

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

# 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