### 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
- 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

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

# 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