### Archives

### Recent blog posts

- 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
- PFA and the tree property at $\aleph_2$ June 9, 2013

### Keywords

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

## Jensen’s diamond principle and its relatives

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading

Posted in Open Problems, Publications
Tagged 03E05, 03E35, 03E50, approachability ideal, Club Guessing, Diamond, diamond star, Non-saturation, sap, Souslin Tree, square, stationary hitting, Uniformization, Whitehead Problem
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## A relative of the approachability ideal, diamond and non-saturation

Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading