### 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

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

- Luzin sets and generalizations
- Nonuniversal colorings in ZFC
- Large Sets
- Infinite-dimensional Jonsson algebras
- Strong colorings without nontrivial polychromatic sets
- Infinite-dimensional polychromatic colorings
- Polychromatic colorings of the first uncountable cardinal
- From colorings to topology
- From topology to colorings
- Anti-Ramsey colorings of the rational numbers, part 2

# 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