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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# Tag Archives: Whitehead Problem

## 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

## Shelah’s solution to Whitehead’s problem

Whitehead problem notes in hebrew : Table of contents Chapter 0 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 References