### 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
- Generalizations 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

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

# 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