### 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

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

# 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