Work

General Criterion for a Poset to Admit a Partition Into $ω$-Chains

Year: 2026

Type: preprint

Abstract: Given a poset $P$ with no maximal element the question naturally arises of when $P$ can be partitioned into $ω$-chains. In this paper we give general criterion for when this can be done. We show that in the case when a poset with no maximal element is countable or a well-founded forest, then it can always be partitioned into $ω$-chains. We then introduce the lifting property for posets with no maximal element and show that a poset can be partitioned into $ω$-chains if and only if it has the lifting property.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29056

Author: Schmeis, Remi Salinas

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, New Mexico State University

Award: RTG: Research Training Group in Logic and its Application

OpenAlex ID: W7223212527

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