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

# 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