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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

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

# Tag Archives: Axiom R

## 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