"arithmetic hierarchy" meaning in English

{
  "forms": [
    {
      "form": "arithmetic hierarchies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "arithmetic hierarchy (plural arithmetic hierarchies)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "alt_of": [
        {
          "word": "arithmetical hierarchy"
        }
      ],
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "Alternative form of arithmetical hierarchy"
      ],
      "id": "en-arithmetic_hierarchy-en-noun-pbjUNXWy",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "arithmetical hierarchy",
          "arithmetical hierarchy#English"
        ]
      ],
      "raw_glosses": [
        "(logic) Alternative form of arithmetical hierarchy"
      ],
      "tags": [
        "alt-of",
        "alternative"
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ]
    }
  ],
  "word": "arithmetic hierarchy"
}

{
  "forms": [
    {
      "form": "arithmetic hierarchies",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "arithmetic hierarchy (plural arithmetic hierarchies)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "alt_of": [
        {
          "word": "arithmetical hierarchy"
        }
      ],
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Logic"
      ],
      "glosses": [
        "Alternative form of arithmetical hierarchy"
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "arithmetical hierarchy",
          "arithmetical hierarchy#English"
        ]
      ],
      "raw_glosses": [
        "(logic) Alternative form of arithmetical hierarchy"
      ],
      "tags": [
        "alt-of",
        "alternative"
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ]
    }
  ],
  "word": "arithmetic hierarchy"
}