### 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
- Generalizations 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

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