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PreprintarXiv licencearXiv

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

  • Remi Salinas Schmeis
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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.

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Cite

BibTeXRIS
BibTeX
@misc{schmeis2026general,
  title = {{General Criterion for a Poset to Admit a Partition Into $ω$-Chains}},
  author = {Remi Salinas Schmeis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29056},
  eprint = {2610.29056},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29056},
}
RIS
TY  - UNPB
TI  - General Criterion for a Poset to Admit a Partition Into ω-Chains
AU  - Remi Salinas Schmeis
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29056
UR  - https://arxiv.org/abs/2610.29056
AB  - 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.
ER  -