### Archives

### Recent blog posts

- More notions of forcing 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

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

# 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