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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

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

# 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