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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
- 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

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

# Tag Archives: free 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