### 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

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

# 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