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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

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

# 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