### 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

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

# 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