### 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

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

# 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