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### Recent blog posts

- 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
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

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

# 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