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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

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

# 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