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### Recent blog posts

- The reflection principle $R_2$ May 20, 2016
- 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

### Keywords

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

# 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