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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

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

# 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