### Archives

### Recent blog posts

- 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

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

# 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

Posted in Ordered Sets, Publications
Tagged 03E04, 03E05, 03E45, 03E55, 03E65, Large Cardinals, Poset, Shelah's Strong Hypothesis, Singular coﬁnality, Singular Density
Leave a comment