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axiom schema of replacement

in set theory, the axiom schema that the image of a set under a definable class function is also a set
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axiom schema of replacement

Summary

axiom schema of replacement is an axiom schema[1]. It draws 94 Wikipedia views per month (axiom_schema category, ranking #2 of 2).[2]

Key Facts

  • axiom schema of replacement is credited with the discovery of Abraham Fraenkel[3].
  • axiom schema of replacement's instance of is recorded as axiom schema[4].
  • axiom schema of replacement's subclass of is recorded as axiom[5].
  • axiom schema of replacement's part of is recorded as list of axioms[6].
  • axiom schema of replacement's time of discovery or invention is recorded as +1921-00-00T00:00:00Z[7].
  • axiom schema of replacement's Freebase ID is recorded as /m/0ds27[8].
  • axiom schema of replacement's Encyclopædia Britannica Online ID is recorded as topic/axiom-schema-of-replacement[9].
  • axiom schema of replacement's defining formula is recorded as \forall w_1,\ldots,w_n \, \forall A \, \exists B \, \forall x \, ( x \in B \Leftrightarrow [ x \in A \and \varphi(x, w_1, \ldots, w_n , A) ] )[10].
  • axiom schema of replacement's studied by is recorded as Zermelo–Fraenkel set theory[11].
  • axiom schema of replacement's MathWorld ID is recorded as AxiomofReplacement[12].
  • axiom schema of replacement's Quora topic ID is recorded as Axiom-Schema-of-Replacement[13].
  • axiom schema of replacement's nLab ID is recorded as axiom of replacement[14].
  • axiom schema of replacement's schematic is recorded as Axiom schema of replacement.svg[15].
  • axiom schema of replacement's maintained by WikiProject is recorded as WikiProject Mathematics[16].
  • axiom schema of replacement's Microsoft Academic ID is recorded as 2780877781[17].
  • axiom schema of replacement's ProofWiki ID is recorded as Axiom:Axiom_of_Replacement[18].
  • axiom schema of replacement's Metamath statement ID is recorded as ax-rep[19].

Body

Works and Contributions

axiom schema of replacement is credited with the discovery of Abraham Fraenkel[3].

Why It Matters

axiom schema of replacement draws 94 Wikipedia views per month (axiom_schema category, ranking #2 of 2).[2] It has Wikipedia articles in 16 language editions, a strong signal of global cultural recognition.[20] It is known by 14 alternative names across languages and contexts.[21]

References

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

Direct Wikidata claims

  1. [4] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . Freebase Data Dumps. wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . Quora. wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . wikidata.org.
  14. [16] ↑ . wikidata.org.
  15. [17] ↑ . wikidata.org.
  16. [18] ↑ . wikidata.org.
  17. [19] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [20] ↑ . Wikidata sitelinks. wikidata.org.
  3. [21] ↑ . 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). axiom schema of replacement. Retrieved May 3, 2026, from https://4ort.xyz/entity/axiom-schema-of-replacement
MLA “axiom schema of replacement.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/axiom-schema-of-replacement.
BibTeX @misc{4ortxyz_axiom-schema-of-replacement_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{axiom schema of replacement}}, year = {2026}, url = {https://4ort.xyz/entity/axiom-schema-of-replacement}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): axiom schema of replacement — https://4ort.xyz/entity/axiom-schema-of-replacement (retrieved 2026-05-03)

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