### 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

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

# 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
2 Comments

## 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