### Archives

### 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

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

# 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