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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
- Genearlizations 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

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

# Tag Archives: Martin’s Axiom

## Genearlizations 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