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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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