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ultraproduct

quotient of the direct product of a family of structures by an ultrafilter
Class type of: structure Q1535225

Facts

5 properties
Subclass of
structure[1]
Defining formula
\frac{\prod_{i\in I}M_i}{a\sim b\iff\left\{i\in I\colon a_i=b_i\right\}\in U}[2]
In defining formula
U, I, M_i, \sim[5][6][7][8]
Maintained by WikiProject
WikiProject Mathematics[4]
Studied by
model theory[3]
🏷️ Also known as
en ultrapower en ultraproduct de Ultraprodukt fi ultratulo fr ultraproduit he על־מכפלה he על מכפלה he על-מכפלה it ultraprodotto ja 超冪構成 ja 超積 ko 초곱 ru сверхпроизведенеие ru ультрапроизведение
🔖 Identifiers · 7
OpenAlex ID
C167930466
Encyclopædia Britannica Online ID
topic/ultrapower, topic/ultraproduct
Freebase ID
/m/01p1l1
MathWorld ID
Ultraproduct
Microsoft Academic ID (discontinued)
167930466
NLab ID
ultraproduct
ScienceDirect topic ID
mathematics/ultraproduct

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🔗 Connections
Maintained by WikiProject 1
WikiProject Mathematics
Studied by 1
model theory
Subclass of 1
structure
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References

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

Direct Wikidata claims

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

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APA 4ort.xyz Knowledge Graph. (2026). ultraproduct. Retrieved November 10, 2026, from https://4ort.xyz/entity/ultraproduct
MLA “ultraproduct.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Nov. 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: 2026-11-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): ultraproduct — https://4ort.xyz/entity/ultraproduct (retrieved 2026-11-10)

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