{
  "aliases": [
    "computably-isomorphic",
    "recursive-isomorphism",
    "recursively-isomorphic"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn computability theory two sets $A, B$ of [[natural numbers|0MWKJ44V5A]] are **computably isomorphic** or **recursively isomorphic** if there exists a total computable and bijective function $f \\colon \\mathbb{N} \\to \\mathbb{N}$ such that the image of $f$ restricted to $A\\subseteq \\mathbb{N}$ equals $B\\subseteq \\mathbb{N}$, i.e. $f(A) = B$.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "aliases": [
      "computably-isomorphic",
      "recursive-isomorphism",
      "recursively-isomorphic"
    ],
    "inventory": [
      "CM16KM9AT0"
    ],
    "kind": "concept",
    "name": "Computable isomorphism",
    "same_as": {
      "wikidata": "Q5157265",
      "wikipedia": "Computable isomorphism"
    },
    "sources": [
      {
        "locator": "Computable isomorphism",
        "mention": "wikipedia://en/2611685",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:2611685@r1322667615"
      }
    ],
    "tag": "4XPS4W1T1K"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/4XPS4W1T1K/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/4XPS4W1T1K.md",
  "msc": null,
  "name": "Computable isomorphism",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/4XP/4XPS4W1T1K.md",
  "status": null,
  "tag": "4XPS4W1T1K",
  "uri": "m2://4XPS4W1T1K",
  "url": "https://math2.tamnd.com/wiki/computable-isomorphism/",
  "writing": {
    "tag": "4XPS4W1T1K",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}