"urelement" meaning in English

{
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        "1": "en",
        "2": "ur",
        "3": "element",
        "t1": "primordial"
      },
      "expansion": "ur- (“primordial”) + element",
      "name": "prefix"
    }
  ],
  "etymology_text": "From ur- (“primordial”) + element.",
  "forms": [
    {
      "form": "urelements",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "urelement (plural urelements)",
      "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"
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          "source": "w"
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          "kind": "other",
          "name": "English terms prefixed with ur-",
          "parents": [],
          "source": "w"
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          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
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            "Formal sciences",
            "Sciences",
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            "Fundamental"
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      "derived": [
        {
          "word": "KPU"
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        {
          "word": "NFU"
        }
      ],
      "examples": [
        {
          "text": "1996, Scientific Books staff (translators), Yuri L. Ershov, Definability and Computability, Scientific Books, page viii,\nThe introduction of urelements would seem to be a technical improvement; however, now we know that just such an extension of the notion of the admissible set led to the universal theory of computability based on the notion of definability by formulas with (in a broad sense) effective semantics."
        },
        {
          "ref": "2012, Nicholas J. J. Smith, Logic: The Laws of Truth, Princeton University Press, page 448",
          "text": "There may be no urelements; as we shall see, we can still build plenty of sets in this case. At stage 0 we can always build the empty set. If there are no urelements, this is the only set we can build. If there is one urelement, a, we can build the sets #x5C;empty and #x5C;#x7B;a#x5C;#x7D;. If there are two urelements, a and b, the possible sets are #x5C;#x7B;a#x5C;#x7D;, #x5C;#x7B;b#x5C;#x7D;, and #x5C;#x7B;a,b#x5C;#x7D;; and so on if there are more urelements.\nAt stage 1, we can build any set containing urelements or sets built at stage 0; that is, any set whose members are already available at the beginning of stage 1. If there are no urelements, we can build #x5C;empty and #x5C;#x7B;#x5C;empty#x5C;#x7D;.",
          "type": "quotation"
        },
        {
          "ref": "2013, Agustín Rayo, The Construction of Logical Space, Oxford University Press, page 95",
          "text": "Let #x5C;mathcal#x7B;L#x7D;#x5C;alpha#x5F;#x5C;in be a version of the language of set-theory with urelements in which each occurrence of a quantifier is restricted by some V#x5F;#x5C;beta (#x5C;beta#x3C;#x5C;alpha).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A mathematical object which is not a set but which can be an element of a set."
      ],
      "id": "en-urelement-en-noun-X3Dvne44",
      "links": [
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          "set theory",
          "set theory"
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          "set",
          "set"
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      "raw_glosses": [
        "(set theory) A mathematical object which is not a set but which can be an element of a set."
      ],
      "related": [
        {
          "word": "hereditary set"
        },
        {
          "word": "pure set"
        },
        {
          "word": "Quine atom"
        }
      ],
      "synonyms": [
        {
          "word": "atom"
        },
        {
          "word": "ur-element"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "translations": [
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "mathematical object",
          "tags": [
            "neuter"
          ],
          "word": "frumstak"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "mathematical object",
          "word": "urelemento"
        }
      ]
    }
  ],
  "word": "urelement"
}

{
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    {
      "word": "KPU"
    },
    {
      "word": "NFU"
    }
  ],
  "etymology_templates": [
    {
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        "t1": "primordial"
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      "expansion": "ur- (“primordial”) + element",
      "name": "prefix"
    }
  ],
  "etymology_text": "From ur- (“primordial”) + element.",
  "forms": [
    {
      "form": "urelements",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "urelement (plural urelements)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "hereditary set"
    },
    {
      "word": "pure set"
    },
    {
      "word": "Quine atom"
    }
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  "senses": [
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        "English entries with incorrect language header",
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        "English nouns",
        "English terms prefixed with ur-",
        "English terms with quotations",
        "en:Set theory"
      ],
      "examples": [
        {
          "text": "1996, Scientific Books staff (translators), Yuri L. Ershov, Definability and Computability, Scientific Books, page viii,\nThe introduction of urelements would seem to be a technical improvement; however, now we know that just such an extension of the notion of the admissible set led to the universal theory of computability based on the notion of definability by formulas with (in a broad sense) effective semantics."
        },
        {
          "ref": "2012, Nicholas J. J. Smith, Logic: The Laws of Truth, Princeton University Press, page 448",
          "text": "There may be no urelements; as we shall see, we can still build plenty of sets in this case. At stage 0 we can always build the empty set. If there are no urelements, this is the only set we can build. If there is one urelement, a, we can build the sets #x5C;empty and #x5C;#x7B;a#x5C;#x7D;. If there are two urelements, a and b, the possible sets are #x5C;#x7B;a#x5C;#x7D;, #x5C;#x7B;b#x5C;#x7D;, and #x5C;#x7B;a,b#x5C;#x7D;; and so on if there are more urelements.\nAt stage 1, we can build any set containing urelements or sets built at stage 0; that is, any set whose members are already available at the beginning of stage 1. If there are no urelements, we can build #x5C;empty and #x5C;#x7B;#x5C;empty#x5C;#x7D;.",
          "type": "quotation"
        },
        {
          "ref": "2013, Agustín Rayo, The Construction of Logical Space, Oxford University Press, page 95",
          "text": "Let #x5C;mathcal#x7B;L#x7D;#x5C;alpha#x5F;#x5C;in be a version of the language of set-theory with urelements in which each occurrence of a quantifier is restricted by some V#x5F;#x5C;beta (#x5C;beta#x3C;#x5C;alpha).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A mathematical object which is not a set but which can be an element of a set."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ]
      ],
      "raw_glosses": [
        "(set theory) A mathematical object which is not a set but which can be an element of a set."
      ],
      "synonyms": [
        {
          "word": "atom"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "ur-element"
    }
  ],
  "translations": [
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "mathematical object",
      "tags": [
        "neuter"
      ],
      "word": "frumstak"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "mathematical object",
      "word": "urelemento"
    }
  ],
  "word": "urelement"
}