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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

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

# 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