### Archives

### 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

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

# 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