### 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

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

# 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