### 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

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

# 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