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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

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

# 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