"Peano arithmetic" meaning in English

{
  "etymology_templates": [
    {
      "args": {
        "1": "mathematician",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "mathematician",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano"
      },
      "expansion": "Giuseppe Peano",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano",
        "born": "1858",
        "died": "1932",
        "nat": "Italian",
        "occ": "mathematician",
        "wplink": "="
      },
      "expansion": "Named after Italian mathematician Giuseppe Peano (1858–1932)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after Italian mathematician Giuseppe Peano (1858–1932).",
  "forms": [
    {
      "form": "Peano arithmetics",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "Peano arithmetic (countable and uncountable, plural Peano arithmetics)",
      "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": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Polish translations",
          "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 axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "id": "en-Peano_arithmetic-en-noun-TlRWJf~x",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "first-order logic",
          "first-order logic"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "successor",
          "successor"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "related": [
        {
          "word": "Presburger arithmetic"
        }
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "Peanon aritmetiikka"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Peanoarithmetik"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "arytmetyka Peana"
        }
      ],
      "wikipedia": [
        "Peano arithmetic"
      ]
    }
  ],
  "word": "Peano arithmetic"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "mathematician",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "mathematician",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano"
      },
      "expansion": "Giuseppe Peano",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano",
        "born": "1858",
        "died": "1932",
        "nat": "Italian",
        "occ": "mathematician",
        "wplink": "="
      },
      "expansion": "Named after Italian mathematician Giuseppe Peano (1858–1932)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after Italian mathematician Giuseppe Peano (1858–1932).",
  "forms": [
    {
      "form": "Peano arithmetics",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "Peano arithmetic (countable and uncountable, plural Peano arithmetics)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Presburger arithmetic"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English uncountable nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Finnish translations",
        "Terms with German translations",
        "Terms with Polish translations",
        "Translation table header lacks gloss",
        "en:Logic"
      ],
      "glosses": [
        "A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "first-order logic",
          "first-order logic"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "successor",
          "successor"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Peano arithmetic"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "Peanon aritmetiikka"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Peanoarithmetik"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "arytmetyka Peana"
    }
  ],
  "word": "Peano arithmetic"
}