### Archives

### 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

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

# 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