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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

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

# 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