### 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

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

# 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