{
  "aliases": [
    "kalmar-functions"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nThe term **elementary** was originally introduced by László Kalmár in the context of computability theory. He defined the class of **elementary recursive functions** (*\"Kalmár elementary functions\"*) as a subset of the primitive recursive functions — specifically, those that can be computed using a limited set of operations such as composition, bounded sums, and bounded products. These functions grow no faster than a fixed-height tower of exponentiation (for example, $O(2^{2^n})$). Not all primitive recursive functions are elementary; for example, tetration grows too rapidly to be included in the elementary class. The elementary recursive functions correspond to the class $\\mathcal{E}^3$ of the Grzegorczyk hierarchy.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "aliases": [
      "kalmar-functions"
    ],
    "inventory": [
      "R58F0CHQTG"
    ],
    "kind": "concept",
    "name": "Elementary recursive function",
    "same_as": {
      "wikidata": "Q5323278",
      "wikipedia": "Elementary recursive function"
    },
    "sources": [
      {
        "locator": "Elementary recursive function",
        "mention": "wikipedia://en/665096",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:665096@r1369784560"
      }
    ],
    "tag": "RJ3MCAAZSV"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/RJ3MCAAZSV/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/RJ3MCAAZSV.md",
  "msc": null,
  "name": "Elementary recursive function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/RJ3/RJ3MCAAZSV.md",
  "status": null,
  "tag": "RJ3MCAAZSV",
  "uri": "m2://RJ3MCAAZSV",
  "url": "https://math2.tamnd.com/wiki/elementary-recursive-function/",
  "writing": {
    "tag": "RJ3MCAAZSV",
    "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
      }
    ]
  }
}
