### 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

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

# 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