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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
- Generalizations 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

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

# Tag Archives: 03E50

## 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