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### Recent blog posts

- 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
- Polychromatic colorings November 26, 2013

### Keywords

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

# 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