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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

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

# Tag Archives: 03G05

## 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