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proper forcing axiom

set theory axiom that if 𝑃 is a proper forcing and 𝐷(𝛼) is a dense subset of 𝑃 for each 𝛼<ω₁, then there is a filter πΊβŠ†π‘ƒ such that 𝐷(𝛼)∩𝐺 is nonempty for all 𝛼<ω₁
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proper forcing axiom

Summary

proper forcing axiom is an axiom of set theory[1]. It draws 15 Wikipedia views per month (axiom_of_set_theory category, ranking #13 of 17).[2]

Key Facts

  • proper forcing axiom's instance of is recorded as axiom of set theory[3].
  • proper forcing axiom's Freebase ID is recorded as /m/0fyy7q[4].
  • proper forcing axiom's short name is recorded as {'lang': 'en', 'text': 'PFA'}[5].
  • proper forcing axiom's maintained by WikiProject is recorded as WikiProject Mathematics[6].
  • proper forcing axiom's Microsoft Academic ID is recorded as 2776548258[7].
  • proper forcing axiom's logical consequence of is recorded as list of values as qualifiers[8].

Why It Matters

proper forcing axiom draws 15 Wikipedia views per month (axiom_of_set_theory category, ranking #13 of 17).[2]

References

Programmatic citations β€” 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.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.

πŸ“‘ 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). proper forcing axiom. Retrieved May 3, 2026, from https://4ort.xyz/entity/proper-forcing-axiom
MLA “proper forcing axiom.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/proper-forcing-axiom.
BibTeX @misc{4ortxyz_proper-forcing-axiom_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{proper forcing axiom}}, year = {2026}, url = {https://4ort.xyz/entity/proper-forcing-axiom}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): proper forcing axiom — https://4ort.xyz/entity/proper-forcing-axiom (retrieved 2026-05-03)

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