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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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