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### Recent blog posts

- Prolific Souslin trees March 17, 2016
- 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

### Keywords

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

## 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