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### 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

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

# Tag Archives: projective Boolean algebra

## 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