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### Recent blog posts

- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- 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

### Keywords

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

# 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

## 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