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### Recent blog posts

- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013

### Keywords

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