### 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
- 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

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

# 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