"elementary equivalence" meaning in All languages combined

{
  "forms": [
    {
      "form": "elementary equivalences",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "elementary equivalence (plural elementary equivalences)",
      "name": "en-noun"
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  ],
  "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"
        },
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          "kind": "other",
          "name": "Terms with Finnish translations",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "glosses": [
        "A relation between two structures which have the property that every first-order formula is valid in one structure if and only if it is valid in the other."
      ],
      "id": "en-elementary_equivalence-en-noun-FW0TNac1",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "relation",
          "relation"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "property",
          "property"
        ],
        [
          "first-order",
          "first-order"
        ],
        [
          "formula",
          "formula"
        ],
        [
          "valid",
          "valid"
        ],
        [
          "if and only if",
          "if and only if"
        ]
      ],
      "raw_glosses": [
        "(logic) A relation between two structures which have the property that every first-order formula is valid in one structure if and only if it is valid in the other."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "relation between logical structures",
          "word": "elementaarinen ekvivalenssi"
        }
      ],
      "wikipedia": [
        "elementary equivalence"
      ]
    }
  ],
  "word": "elementary equivalence"
}

{
  "forms": [
    {
      "form": "elementary equivalences",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "elementary equivalence (plural elementary equivalences)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Terms with Finnish translations",
        "en:Logic"
      ],
      "glosses": [
        "A relation between two structures which have the property that every first-order formula is valid in one structure if and only if it is valid in the other."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "relation",
          "relation"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "property",
          "property"
        ],
        [
          "first-order",
          "first-order"
        ],
        [
          "formula",
          "formula"
        ],
        [
          "valid",
          "valid"
        ],
        [
          "if and only if",
          "if and only if"
        ]
      ],
      "raw_glosses": [
        "(logic) A relation between two structures which have the property that every first-order formula is valid in one structure if and only if it is valid in the other."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "elementary equivalence"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "relation between logical structures",
      "word": "elementaarinen ekvivalenssi"
    }
  ],
  "word": "elementary equivalence"
}