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### Recent blog posts

- 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
- Universal binary sequences November 14, 2013

### Keywords

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

# 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