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### 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

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

# 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