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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

### Keywords

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

# 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