### Archives

### Recent blog posts

- 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
- Walk on countable ordinals: the characteristics December 1, 2013

### Keywords

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

# 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