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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

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

# 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