### 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
- 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

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

# Tag Archives: 03E55

## Openly generated Boolean algebras and the Fodor-type reflection principle

Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading