{
  "aliases": [
    "computably-inseparable-sets",
    "effectively-inseparable",
    "effectively-inseparable-sets",
    "effectively-separable",
    "effectively-separable-set",
    "effectively-separable-sets",
    "recursive-inseparability",
    "recursively-inseparable",
    "recursively-inseparable-sets",
    "recursively-separable",
    "recursively-separable-sets"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn computability theory, two [[disjoint sets|0W4RPA8QH3]] of natural numbers are called **computably inseparable** or **recursively inseparable** if they cannot be \"separated\" with a computable set. These sets arise in the study of computability theory itself, particularly in relation to $\\Pi^0_1$ classes. Computably inseparable sets also arise in the study of Gödel's incompleteness theorem.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "aliases": [
      "computably-inseparable-sets",
      "effectively-inseparable",
      "effectively-inseparable-sets",
      "effectively-separable",
      "effectively-separable-set",
      "effectively-separable-sets",
      "recursive-inseparability",
      "recursively-inseparable",
      "recursively-inseparable-sets",
      "recursively-separable",
      "recursively-separable-sets"
    ],
    "inventory": [
      "SSRVGHP7Y5"
    ],
    "kind": "concept",
    "name": "Computably inseparable",
    "same_as": {
      "wikidata": "Q7303355",
      "wikipedia": "Computably inseparable"
    },
    "sources": [
      {
        "locator": "Computably inseparable",
        "mention": "wikipedia://en/26004614",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:26004614@r1298641139"
      }
    ],
    "tag": "1HXBZNJQDX"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/1HXBZNJQDX/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/1HXBZNJQDX.md",
  "msc": null,
  "name": "Computably inseparable",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/1HX/1HXBZNJQDX.md",
  "status": null,
  "tag": "1HXBZNJQDX",
  "uri": "m2://1HXBZNJQDX",
  "url": "https://math2.tamnd.com/wiki/computably-inseparable/",
  "writing": {
    "tag": "1HXBZNJQDX",
    "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
      }
    ]
  }
}