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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

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

# 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