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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

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

# 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