### 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

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

# Tag Archives: free Boolean algebra

## 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