### 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

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

# 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 Publications
Tagged 03E04, 03E05, 03E45, 03E55, 03E65, Large Cardinals, Poset, Shelah's Strong Hypothesis, Singular Cofinality, Singular Density
Leave a comment