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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

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

# 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