Robinson arithmetic

finitely axiomatized fragment of first-order Peano arithmetic that is recursively incompletable (in the sense of Gödel’s incompleteness theorems) and essentially undecidable
Thing axiomatic_system Q928884
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Robinson arithmetic

Summary

Robinson arithmetic is an axiomatic system[1]. It draws 95 Wikipedia views per month (axiomatic_system category, ranking #4 of 12).[2]

Key Facts

  • Robinson arithmetic's instance of is recorded as axiomatic system[3].
  • Raphael M. Robinson is named after Robinson arithmetic[4].
  • Robinson arithmetic's Freebase ID is recorded as /m/07m3f2[5].
  • Robinson arithmetic's defining formula is recorded as \begin{align}&Sx\ne0\&Sx=Sy\implies x=y\&y=0\lor \exists x.(Sx=y)\&x+0=x\&x+Sy=S(x+y)\&x\cdot0=0\&x\cdot Sy=(x\cdot y)+x\end{align}[6].
  • Robinson arithmetic's nLab ID is recorded as Robinson arithmetic[7].
  • Robinson arithmetic's Microsoft Academic ID is recorded as 4962995[8].
  • Robinson arithmetic's does not have characteristic is recorded as decidability[9].
  • Robinson arithmetic's in defining formula is recorded as S[10].
  • Robinson arithmetic's in defining formula is recorded as 0[11].
  • Robinson arithmetic's in defining formula is recorded as +[12].
  • Robinson arithmetic's in defining formula is recorded as \cdot[13].
  • Robinson arithmetic's in defining formula is recorded as \lor[14].
  • Robinson arithmetic's in defining formula is recorded as \implies[15].
  • Robinson arithmetic's in defining formula is recorded as \exists[16].

Why It Matters

Robinson arithmetic draws 95 Wikipedia views per month (axiomatic_system category, ranking #4 of 12).[2] It has Wikipedia articles in 7 language editions, a strong signal of global cultural recognition.[17]

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] . Freebase Data Dumps. 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.

Class ancestry

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

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [17] . Wikidata sitelinks. 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). Robinson arithmetic. Retrieved May 3, 2026, from https://4ort.xyz/entity/robinson-arithmetic
MLA “Robinson arithmetic.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/robinson-arithmetic.
BibTeX @misc{4ortxyz_robinson-arithmetic_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Robinson arithmetic}}, year = {2026}, url = {https://4ort.xyz/entity/robinson-arithmetic}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Robinson arithmetic — https://4ort.xyz/entity/robinson-arithmetic (retrieved 2026-05-03)

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