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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

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

# Tag Archives: Axiom R

## 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