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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

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

# 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