### 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

Fodor-type reflection ccc Constructible Universe Erdos Cardinal Commutative cancellative semigroups PFA Diamond very good scale middle diamond Almost-disjoint famiy tensor product graph P-Ideal Dichotomy b-scale Dushnik-Miller Chang's conjecture Microscopic Approach approachability ideal weak diamond Singular Density Small forcing coloring number Almost countably chromatic Poset Sakurai's Bell inequality Almost Souslin HOD Parameterized proxy principle Generalized Clubs Reduced Power weak square Aronszajn tree PFA(S)[S] Cardinal function Fast club Square-Brackets Partition Relations 20M14 Ostaszewski square Prevalent singular cardinals incompactness Non-saturation Minimal Walks Selective Ultrafilter square Shelah's Strong Hypothesis L-space Hereditarily Lindelöf space Absoluteness Whitehead Problem Jonsson cardinal stationary hitting Slim tree Cohen real Cardinal Invariants Forcing Singular Cofinality stationary reflection 11P99 Ascent Path S-Space Weakly compact cardinal Rock n' Roll projective Boolean algebra Martin's Axiom Successor of Singular Cardinal Large Cardinals Foundations Uniformization Kurepa Hypothesis Souslin Tree Fat stationary set reflection principles Stevo Todorcevic free Boolean algebra Forcing Axioms Singular coﬁnality Coherent tree Antichain Mandelbrot set Partition Relations Successor of Regular Cardinal Universal Sequences 05A17 Singular cardinals combinatorics Hedetniemi's conjecture polarized partition relation Axiom R sap diamond star Chromatic number Rainbow sets Rado's conjecture Hindman's Theorem 05D10 Erdos-Hajnal graphs Club Guessing OCA xbox Prikry-type forcing Knaster

# 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