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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

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

# 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