### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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