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### Recent blog posts

- More notions of forcing add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Genearlizations 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

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

# 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