### 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

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

# 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