### Archives

### 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

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

# 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