### 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

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

# 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