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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- 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

### Keywords

Rado's conjecture Dushnik-Miller approachability ideal Commutative cancellative semigroups Jonsson cardinal P-Ideal Dichotomy b-scale Weakly compact cardinal Generalized Clubs Singular Density ccc Hedetniemi's conjecture very good scale Rainbow sets tensor product graph PFA reflection principles Microscopic Approach Axiom R 20M14 projective Boolean algebra Universal Sequences Square-Brackets Partition Relations 05A17 Almost-disjoint famiy sap Singular coﬁnality Constructible Universe Souslin Tree Martin's Axiom Uniformization Singular Cofinality Large Cardinals Parameterized proxy principle 05D10 Forcing Hereditarily Lindelöf space Successor of Singular Cardinal Minimal Walks polarized partition relation Aronszajn tree Foundations Chang's conjecture free Boolean algebra Singular cardinals combinatorics Selective Ultrafilter Club Guessing Mandelbrot set weak diamond 11P99 Stevo Todorcevic L-space incompactness Fast club Ascent Path Coherent tree Cardinal function Prikry-type forcing stationary reflection Antichain Whitehead Problem Forcing Axioms square HOD S-Space Almost Souslin Chromatic number weak square Fat stationary set Rock n' Roll OCA Shelah's Strong Hypothesis Successor of Regular Cardinal middle diamond Partition Relations Small forcing stationary hitting PFA(S)[S] Cardinal Invariants Knaster Diamond Hindman's Theorem Reduced Power Poset Slim tree Almost countably chromatic Cohen real Erdos Cardinal Kurepa Hypothesis Non-saturation Absoluteness Erdos-Hajnal graphs Ostaszewski square Sakurai's Bell inequality diamond star Prevalent singular cardinals xbox

# 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