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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

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

# Tag Archives: Martin’s Axiom

## Generalizations of Martin’s Axiom and the well-met condition

Recall that Martin’s Axiom asserts that for every partial order $\mathbb P$ satisfying c.c.c., and for any family $\mathcal D$ of $<2^{\aleph_0}$ many dense subsets of $\mathbb P$, there exists a directed subset $G$ of $\mathbb P$ such that $G\cap … 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