Kojiro Higuchi

collaborators

2 papers

math.LO2023

A Note on a Conjecture of Sacks: It is Harder to Embed Height Three Partial Orders than Height Two Partial Orders

Kojiro Higuchi, Patrick Lutz

A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable partial order of size continuum embeds into the Turing degrees. We show that this…

math.LO2019

On the order dimension of locally countable partial orderings

Kojiro Higuchi, Steffen Lempp, Diip Raghavan +1

We show that the order dimension of the partial order of all finite subsets of $κ$ under set inclusion is $lo g_{2} (lo g_{2} (κ))$ whenever $κ$ is an infinite cardinal. We also…