### 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
- 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

### Keywords

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

# 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