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### Recent blog posts

- 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
- Polychromatic colorings November 26, 2013

### Keywords

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

# 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