### 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

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

# 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