### 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

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

# 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