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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

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

# Tag Archives: 03E55

## 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

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading