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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

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

# 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