Zermelo–Fraenkel set theory

variant of ZFC, the standard axiomatic set theory
Thing set_theory Q191849
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Zermelo–Fraenkel set theory

Summary

Zermelo–Fraenkel set theory is a set theory[1]. It has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[2]

Key Facts

  • Zermelo–Fraenkel set theory's instance of is recorded as set theory[3].
  • Abraham Fraenkel is named after Zermelo–Fraenkel set theory[4].
  • Ernst Zermelo is named after Zermelo–Fraenkel set theory[5].
  • Zermelo–Fraenkel set theory comprises Zermelo set theory[6].
  • Zermelo–Fraenkel set theory's topic's main category is recorded as Category:Zermelo–Fraenkel set theory[7].
  • Zermelo–Fraenkel set theory's different from is recorded as Zermelo–Fraenkel set theory with choice[8].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom of extensionality[9].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom of regularity[10].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom schema of specification[11].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom of pairing[12].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom of union[13].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom schema of replacement[14].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom of infinity[15].
  • Zermelo–Fraenkel set theory's is the study of is recorded as axiom of power set[16].
  • Zermelo–Fraenkel set theory's maintained by WikiProject is recorded as WikiProject Mathematics[17].

Body

Definition and Type

Zermelo–Fraenkel set theory's instance of is recorded as set theory[3].

Origins

Things named after include Abraham Fraenkel[4], a mathematician[18], 1891–1965[19], of German Reich[20], awarded the Israel Prize[21], specialised in set theory[22] and Ernst Zermelo[5], a mathematician[23], 1871–1953[24], of Germany[25], awarded the Ackermann–Teubner Memorial Award[26], specialised in mathematical logic[27].

Use and Application

Zermelo–Fraenkel set theory comprises Zermelo set theory[6].

Why It Matters

Zermelo–Fraenkel set theory has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[2] It is known by 22 alternative names across languages and contexts.[28]

References

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

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.

Inline context (facts about related entities)

  1. [18] . Wikidata. wikidata.org. → on this site
  2. [19] . Wikidata. wikidata.org. → on this site
  3. [20] . Wikidata. wikidata.org. → on this site
  4. [21] . Wikidata. wikidata.org. → on this site
  5. [22] . Wikidata. wikidata.org. → on this site
  6. [23] . Wikidata. wikidata.org. → on this site
  7. [24] . Wikidata. wikidata.org. → on this site
  8. [25] . Wikidata. wikidata.org. → on this site
  9. [26] . Wikidata. wikidata.org. → on this site
  10. [27] . Wikidata. wikidata.org. → on this site

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikidata sitelinks. wikidata.org.
  2. [28] . 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). Zermelo–Fraenkel set theory. Retrieved May 3, 2026, from https://4ort.xyz/entity/zermelo-fraenkel-set-theory
MLA “Zermelo–Fraenkel set theory.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/zermelo-fraenkel-set-theory.
BibTeX @misc{4ortxyz_zermelo-fraenkel-set-theory_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Zermelo–Fraenkel set theory}}, year = {2026}, url = {https://4ort.xyz/entity/zermelo-fraenkel-set-theory}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Zermelo–Fraenkel set theory — https://4ort.xyz/entity/zermelo-fraenkel-set-theory (retrieved 2026-05-03)

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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. 5d ago · HelloImSteven · 2026-06-27 view diff on Wikidata ↗
    Instance of
    Maintained by wikiproject WikiProject Mathematics
    Mathworld id Zermelo-FraenkelSetTheory
    Instance of set theory
    + 9 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:1||1 */ [[Property:P12946]]: Zermelo+Fränkel+set+theory, import/update FOLDOC ID"
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