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### Recent blog posts

- 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
- Walk on countable ordinals: the characteristics December 1, 2013

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

# 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