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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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