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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

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

# Tag Archives: 06E05

## 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