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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

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

# 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