On the order dimension of locally countable partial orderings
Kojiro Higuchi, Steffen Lempp, Diip Raghavan, Frank Stephan · arXiv (Cornell University) · 2019
We show that the order dimension of the partial order of all finite subsets of $κ$ under set inclusion is ${\log}_{2}({\log}_{2}(κ))$ whenever $κ$ is an infinite cardinal. We also show that the order dimension of any locally countable partial ordering $(P,