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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

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

# Tag Archives: projective Boolean algebra

## 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