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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

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

# 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