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

# 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