"подмножеством" meaning in Russian

{
  "forms": [
    {
      "form": "подмно́жеством",
      "tags": [
        "canonical"
      ]
    },
    {
      "form": "podmnóžestvom",
      "tags": [
        "romanization"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "ru",
        "2": "noun form",
        "g": "n-in",
        "head": "подмно́жеством"
      },
      "expansion": "подмно́жеством • (podmnóžestvom) n inan",
      "name": "head"
    }
  ],
  "lang": "Russian",
  "lang_code": "ru",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Russian entries with incorrect language header",
          "parents": [],
          "source": "w"
        }
      ],
      "form_of": [
        {
          "extra": "podmnóžestvo",
          "word": "подмно́жество"
        }
      ],
      "glosses": [
        "instrumental singular of подмно́жество (podmnóžestvo)"
      ],
      "id": "en-подмножеством-ru-noun-EdID~OM3",
      "links": [
        [
          "подмно́жество",
          "подмножество#Russian"
        ]
      ],
      "tags": [
        "form-of",
        "instrumental",
        "singular"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "[pɐdˈmnoʐɨstvəm]"
    }
  ],
  "word": "подмножеством"
}

{
  "forms": [
    {
      "form": "подмно́жеством",
      "tags": [
        "canonical"
      ]
    },
    {
      "form": "podmnóžestvom",
      "tags": [
        "romanization"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "ru",
        "2": "noun form",
        "g": "n-in",
        "head": "подмно́жеством"
      },
      "expansion": "подмно́жеством • (podmnóžestvom) n inan",
      "name": "head"
    }
  ],
  "lang": "Russian",
  "lang_code": "ru",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "Pages with 1 entry",
        "Pages with entries",
        "Russian 4-syllable words",
        "Russian entries with incorrect language header",
        "Russian non-lemma forms",
        "Russian noun forms",
        "Russian terms with IPA pronunciation"
      ],
      "form_of": [
        {
          "extra": "podmnóžestvo",
          "word": "подмно́жество"
        }
      ],
      "glosses": [
        "instrumental singular of подмно́жество (podmnóžestvo)"
      ],
      "links": [
        [
          "подмно́жество",
          "подмножество#Russian"
        ]
      ],
      "tags": [
        "form-of",
        "instrumental",
        "singular"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "[pɐdˈmnoʐɨstvəm]"
    }
  ],
  "word": "подмножеством"
}