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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

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

# 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