On the order dimension of locally countable partial orderings

2019/02/16 by Kojiro Higuchi, Steffen Lempp, Higuchi, Kojiro +5
Computer Science · Mathematics · #03E04 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Primary: 06A06 #Secondary: 03D28 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1902.06030

openalex publication_date 2019/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the order dimension of the partial order of all finite subsets of κ under set inclusion is log₂(log₂(κ)) whenever κ is an infinite cardinal. We also show that the order dimension of any locally countable partial ordering (P,

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