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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

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

# 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