### Archives

### 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
- Genearlizations 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

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

# 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