ultraproduct

quotient of the direct product of a family of structures by an ultrafilter
Thing general Q1535225
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ultraproduct

Summary

ultraproduct ranks in the top 2% of general entities by monthly Wikipedia readership (52 views/month).[1]

Key Facts

  • ultraproduct's subclass of is recorded as structure[2].
  • ultraproduct's Freebase ID is recorded as /m/01p1l1[3].
  • ultraproduct's Encyclopædia Britannica Online ID is recorded as topic/ultrapower[4].
  • ultraproduct's Encyclopædia Britannica Online ID is recorded as topic/ultraproduct[5].
  • ultraproduct's defining formula is recorded as \frac{\prod_{i\in I}M_i}{a\sim b\iff\left{i\in I\colon a_i=b_i\right}\in U}[6].
  • ultraproduct's studied by is recorded as model theory[7].
  • ultraproduct's MathWorld ID is recorded as Ultraproduct[8].
  • ultraproduct's nLab ID is recorded as ultraproduct[9].
  • ultraproduct's maintained by WikiProject is recorded as WikiProject Mathematics[10].
  • ultraproduct's Microsoft Academic ID is recorded as 167930466[11].
  • ultraproduct's in defining formula is recorded as U[12].
  • ultraproduct's in defining formula is recorded as I[13].
  • ultraproduct's in defining formula is recorded as M_i[14].
  • ultraproduct's in defining formula is recorded as \sim[15].
  • ultraproduct's OpenAlex ID is recorded as C167930466[16].
  • ultraproduct's ScienceDirect topic ID is recorded as mathematics/ultraproduct[17].

Why It Matters

ultraproduct ranks in the top 2% of general entities by monthly Wikipedia readership (52 views/month).[1] ultraproduct has Wikipedia articles in 11 language editions, a strong signal of global cultural recognition.[18] ultraproduct is known by 5 alternative names across languages and contexts.[19]

References

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

Direct Wikidata claims

  1. [2] . wikidata.org.
  2. [3] . Freebase Data Dumps. wikidata.org.
  3. [4] . wikidata.org.
  4. [5] . wikidata.org.
  5. [6] . wikidata.org.
  6. [7] . wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . wikidata.org.
  12. [13] . wikidata.org.
  13. [14] . wikidata.org.
  14. [15] . wikidata.org.
  15. [16] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  16. [17] . wikidata.org.

Aggregate / graph-position facts

  1. [1] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [18] . Wikidata sitelinks. wikidata.org.
  3. [19] . 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). ultraproduct. Retrieved April 10, 2026, from https://4ort.xyz/entity/ultraproduct
MLA “ultraproduct.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/ultraproduct.
BibTeX @misc{4ortxyz_ultraproduct_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{ultraproduct}}, year = {2026}, url = {https://4ort.xyz/entity/ultraproduct}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): ultraproduct — https://4ort.xyz/entity/ultraproduct (retrieved 2026-04-10)

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