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partially ordered set

set ordered by a transitive, antisymmetric, and reflexive binary relation
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partially ordered set

Summary

partially ordered set has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[1]

Key Facts

  • partially ordered set is a type of preordered set[2].
  • partially ordered set comprises partial order[3].
  • partially ordered set's Stack Exchange tag is recorded as https://mathoverflow.net/tags/posets[4].
  • partially ordered set's different from is recorded as partial order[5].
  • partially ordered set's studied by is recorded as order theory[6].
  • partially ordered set's maintained by WikiProject is recorded as WikiProject Mathematics[7].
  • partially ordered set's underlying structure is recorded as set[8].

Body

Definition and Type

partially ordered set is a type of preordered set[2].

Use and Application

partially ordered set comprises partial order[3].

Why It Matters

partially ordered set has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[1] It is known by 45 alternative names across languages and contexts.[9]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.
  7. [8] ↑ . Retrieved . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikidata sitelinks. wikidata.org.
  2. [9] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). partially ordered set. Retrieved April 10, 2026, from https://4ort.xyz/entity/partially-ordered-set
MLA “partially ordered set.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/partially-ordered-set.
BibTeX @misc{4ortxyz_partially-ordered-set_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{partially ordered set}}, year = {2026}, url = {https://4ort.xyz/entity/partially-ordered-set}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): partially ordered set — https://4ort.xyz/entity/partially-ordered-set (retrieved 2026-04-10)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 23d ago · Jindřich Rubeš · 2026-06-11 view diff on Wikidata ↗
    Svkkl authority id → 0235199-usporadane-mnoziny
    "/* wbcreateclaim-create:1| */ [[Property:P9322]]: 0235199-usporadane-mnoziny, [[:toollabs:quickstatements/#/batch/259496|batch #259496]]"
  2. 5w ago · Twofivesixbot bot · 2026-05-25 view diff on Wikidata ↗
    Studied by → order theory
    Subclass of → preordered set
    Maintained by wikiproject → WikiProject Mathematics
    Underlying structure(s) → set
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|2 */ [[Property:P8189]]: 987007565496805171, mv to monolingual text names on J9U statements"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.