"arithmetical set" meaning in All languages combined

See arithmetical set on Wiktionary

Noun [English]

Forms: arithmetical sets [plural]
Head templates: {{en-noun}} arithmetical set (plural arithmetical sets)
  1. (logic) A set of natural numbers that can be defined by a formula of first-order Peano arithmetic. Wikipedia link: arithmetical set Categories (topical): Logic Synonyms: arithmetic set Related terms: arithmetical hierarchy
    Sense id: en-arithmetical_set-en-noun-HL-vDeQb Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: human-sciences, logic, mathematics, philosophy, sciences

Inflected forms

{
  "forms": [
    {
      "form": "arithmetical sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "arithmetical set (plural arithmetical sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A set of natural numbers that can be defined by a formula of first-order Peano arithmetic."
      ],
      "id": "en-arithmetical_set-en-noun-HL-vDeQb",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "Peano arithmetic",
          "Peano arithmetic"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of natural numbers that can be defined by a formula of first-order Peano arithmetic."
      ],
      "related": [
        {
          "word": "arithmetical hierarchy"
        }
      ],
      "synonyms": [
        {
          "word": "arithmetic set"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "arithmetical set"
      ]
    }
  ],
  "word": "arithmetical set"
}
{
  "forms": [
    {
      "form": "arithmetical sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "arithmetical set (plural arithmetical sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "arithmetical hierarchy"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Logic"
      ],
      "glosses": [
        "A set of natural numbers that can be defined by a formula of first-order Peano arithmetic."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "Peano arithmetic",
          "Peano arithmetic"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of natural numbers that can be defined by a formula of first-order Peano arithmetic."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "arithmetical set"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "arithmetic set"
    }
  ],
  "word": "arithmetical set"
}

Download raw JSONL data for arithmetical set meaning in All languages combined (1.0kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-08 from the enwiktionary dump dated 2025-01-01 using wiktextract (9a96ef4 and 4ed51a5). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.