"partially ordered set" meaning in English

See partially ordered set in All languages combined, or Wiktionary

Noun

Forms: partially ordered sets [plural]
Head templates: {{en-noun|head=partially ordered set}} partially ordered set (plural partially ordered sets)
  1. (set theory, order theory, loosely) A set that has a given, elsewhere specified partial order. Tags: broadly Categories (topical): Set theory
    Sense id: en-partially_ordered_set-en-noun-icnd8Ckt Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Arabic translations, Terms with Czech translations, Terms with Finnish translations, Terms with German translations, Terms with Japanese translations, Terms with Swedish translations Disambiguation of English entries with incorrect language header: 51 49 Disambiguation of Entries with translation boxes: 53 47 Disambiguation of Pages with 1 entry: 54 46 Disambiguation of Pages with entries: 55 45 Disambiguation of Terms with Arabic translations: 59 41 Disambiguation of Terms with Czech translations: 58 42 Disambiguation of Terms with Finnish translations: 57 43 Disambiguation of Terms with German translations: 57 43 Disambiguation of Terms with Japanese translations: 57 43 Disambiguation of Terms with Swedish translations: 57 43 Topics: mathematics, order-theory, sciences, set-theory
  2. (set theory, order theory, formally) The ordered pair comprising a set and its partial order. Tags: formal Categories (topical): Set theory
    Sense id: en-partially_ordered_set-en-noun-8zd~fBuI Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 51 49 Disambiguation of Entries with translation boxes: 53 47 Disambiguation of Pages with 1 entry: 54 46 Disambiguation of Pages with entries: 55 45 Topics: mathematics, order-theory, sciences, set-theory
The following are not (yet) sense-disambiguated
Synonyms: partially ordered set Synonyms (ordered pair of set and partial order): poset Synonyms (set on which a partial order is defined): ground set, poset Hypernyms: category [order-theory, mathematics, sciences] Hyponyms: lattice [order-theory, mathematics, sciences], totally ordered set [order-theory, mathematics, sciences], complete lattice, distributive lattice, Boolean lattice Related terms: complete partial order, partial order Translations (set having a specified partial order): فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا (fiʔatun murattabatun juzʔiyyan) (english: Arabic Academy term) [feminine] (Arabic), مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا (majmūʕatun murattabatun juzʔiyyan) [common, feminine] (Arabic), uspořádaná množina [feminine] (Czech), osittain järjestetty joukko (Finnish), partiell geordnete Menge [feminine] (German), 半順序集合 (hanjunjo-shūgō) (alt: はんじゅんじょしゅうごう) (Japanese), partiellt ordnad mängd [common-gender] (Swedish)
Disambiguation of 'ordered pair of set and partial order': 45 55 Disambiguation of 'set on which a partial order is defined': 52 48 Disambiguation of 'set having a specified partial order': 52 48

Inflected forms

{
  "forms": [
    {
      "form": "partially ordered sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "partially ordered set"
      },
      "expansion": "partially ordered set (plural partially ordered sets)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "_dis1": "50 50",
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "category"
    }
  ],
  "hyponyms": [
    {
      "_dis1": "50 50",
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "lattice"
    },
    {
      "_dis1": "50 50",
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "totally ordered set"
    },
    {
      "_dis1": "50 50",
      "source": "Thesaurus:partially ordered set",
      "word": "complete lattice"
    },
    {
      "_dis1": "50 50",
      "source": "Thesaurus:partially ordered set",
      "word": "distributive lattice"
    },
    {
      "_dis1": "50 50",
      "source": "Thesaurus:partially ordered set",
      "word": "Boolean lattice"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "_dis1": "50 50",
      "word": "complete partial order"
    },
    {
      "_dis1": "50 50",
      "word": "partial order"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "51 49",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "53 47",
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "54 46",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "55 45",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "59 41",
          "kind": "other",
          "name": "Terms with Arabic translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "58 42",
          "kind": "other",
          "name": "Terms with Czech translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "57 43",
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "57 43",
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "57 43",
          "kind": "other",
          "name": "Terms with Japanese translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "57 43",
          "kind": "other",
          "name": "Terms with Swedish translations",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "A set that has a given, elsewhere specified partial order."
      ],
      "id": "en-partially_ordered_set-en-noun-icnd8Ckt",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ],
        [
          "partial order",
          "partial order"
        ]
      ],
      "raw_glosses": [
        "(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order."
      ],
      "tags": [
        "broadly"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "51 49",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "53 47",
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "54 46",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "55 45",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "text": "1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28,\nA partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of \"≻\" and speak of the partially ordered set P.\nThe ordered fields defined earlier are easily seen to be examples of partially ordered sets."
        },
        {
          "ref": "1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35:",
          "text": "In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.",
          "type": "quote"
        },
        {
          "ref": "2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45:",
          "text": "The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).",
          "type": "quote"
        }
      ],
      "glosses": [
        "The ordered pair comprising a set and its partial order."
      ],
      "id": "en-partially_ordered_set-en-noun-8zd~fBuI",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "ordered pair",
          "ordered pair"
        ]
      ],
      "raw_glosses": [
        "(set theory, order theory, formally) The ordered pair comprising a set and its partial order."
      ],
      "tags": [
        "formal"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ]
    }
  ],
  "synonyms": [
    {
      "_dis1": "52 48",
      "sense": "set on which a partial order is defined",
      "word": "ground set"
    },
    {
      "_dis1": "52 48",
      "sense": "set on which a partial order is defined",
      "word": "poset"
    },
    {
      "_dis1": "45 55",
      "sense": "ordered pair of set and partial order",
      "word": "poset"
    },
    {
      "_dis1": "50 50",
      "source": "Thesaurus:partially ordered set",
      "word": "partially ordered set"
    }
  ],
  "translations": [
    {
      "_dis1": "52 48",
      "code": "ar",
      "english": "Arabic Academy term",
      "lang": "Arabic",
      "roman": "fiʔatun murattabatun juzʔiyyan",
      "sense": "set having a specified partial order",
      "tags": [
        "feminine"
      ],
      "word": "فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
    },
    {
      "_dis1": "52 48",
      "code": "ar",
      "lang": "Arabic",
      "raw_tags": [
        "in educational communities"
      ],
      "roman": "majmūʕatun murattabatun juzʔiyyan",
      "sense": "set having a specified partial order",
      "tags": [
        "common",
        "feminine"
      ],
      "word": "مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
    },
    {
      "_dis1": "52 48",
      "code": "cs",
      "lang": "Czech",
      "sense": "set having a specified partial order",
      "tags": [
        "feminine"
      ],
      "word": "uspořádaná množina"
    },
    {
      "_dis1": "52 48",
      "code": "fi",
      "lang": "Finnish",
      "sense": "set having a specified partial order",
      "word": "osittain järjestetty joukko"
    },
    {
      "_dis1": "52 48",
      "code": "de",
      "lang": "German",
      "sense": "set having a specified partial order",
      "tags": [
        "feminine"
      ],
      "word": "partiell geordnete Menge"
    },
    {
      "_dis1": "52 48",
      "alt": "はんじゅんじょしゅうごう",
      "code": "ja",
      "lang": "Japanese",
      "roman": "hanjunjo-shūgō",
      "sense": "set having a specified partial order",
      "word": "半順序集合"
    },
    {
      "_dis1": "52 48",
      "code": "sv",
      "lang": "Swedish",
      "sense": "set having a specified partial order",
      "tags": [
        "common-gender"
      ],
      "word": "partiellt ordnad mängd"
    }
  ],
  "wikipedia": [
    "partially ordered set"
  ],
  "word": "partially ordered set"
}
{
  "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",
    "Pages with entries",
    "Terms with Arabic translations",
    "Terms with Czech translations",
    "Terms with Finnish translations",
    "Terms with German translations",
    "Terms with Japanese translations",
    "Terms with Swedish translations"
  ],
  "forms": [
    {
      "form": "partially ordered sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "partially ordered set"
      },
      "expansion": "partially ordered set (plural partially ordered sets)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "category"
    }
  ],
  "hyponyms": [
    {
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "lattice"
    },
    {
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "totally ordered set"
    },
    {
      "source": "Thesaurus:partially ordered set",
      "word": "complete lattice"
    },
    {
      "source": "Thesaurus:partially ordered set",
      "word": "distributive lattice"
    },
    {
      "source": "Thesaurus:partially ordered set",
      "word": "Boolean lattice"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "complete partial order"
    },
    {
      "word": "partial order"
    }
  ],
  "senses": [
    {
      "categories": [
        "en:Set theory"
      ],
      "glosses": [
        "A set that has a given, elsewhere specified partial order."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ],
        [
          "partial order",
          "partial order"
        ]
      ],
      "raw_glosses": [
        "(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order."
      ],
      "tags": [
        "broadly"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "en:Set theory"
      ],
      "examples": [
        {
          "text": "1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28,\nA partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of \"≻\" and speak of the partially ordered set P.\nThe ordered fields defined earlier are easily seen to be examples of partially ordered sets."
        },
        {
          "ref": "1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35:",
          "text": "In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.",
          "type": "quote"
        },
        {
          "ref": "2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45:",
          "text": "The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).",
          "type": "quote"
        }
      ],
      "glosses": [
        "The ordered pair comprising a set and its partial order."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "ordered pair",
          "ordered pair"
        ]
      ],
      "raw_glosses": [
        "(set theory, order theory, formally) The ordered pair comprising a set and its partial order."
      ],
      "tags": [
        "formal"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "set on which a partial order is defined",
      "word": "ground set"
    },
    {
      "sense": "set on which a partial order is defined",
      "word": "poset"
    },
    {
      "sense": "ordered pair of set and partial order",
      "word": "poset"
    },
    {
      "source": "Thesaurus:partially ordered set",
      "word": "partially ordered set"
    }
  ],
  "translations": [
    {
      "code": "ar",
      "english": "Arabic Academy term",
      "lang": "Arabic",
      "roman": "fiʔatun murattabatun juzʔiyyan",
      "sense": "set having a specified partial order",
      "tags": [
        "feminine"
      ],
      "word": "فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
    },
    {
      "code": "ar",
      "lang": "Arabic",
      "raw_tags": [
        "in educational communities"
      ],
      "roman": "majmūʕatun murattabatun juzʔiyyan",
      "sense": "set having a specified partial order",
      "tags": [
        "common",
        "feminine"
      ],
      "word": "مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا"
    },
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "set having a specified partial order",
      "tags": [
        "feminine"
      ],
      "word": "uspořádaná množina"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "set having a specified partial order",
      "word": "osittain järjestetty joukko"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "set having a specified partial order",
      "tags": [
        "feminine"
      ],
      "word": "partiell geordnete Menge"
    },
    {
      "alt": "はんじゅんじょしゅうごう",
      "code": "ja",
      "lang": "Japanese",
      "roman": "hanjunjo-shūgō",
      "sense": "set having a specified partial order",
      "word": "半順序集合"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "set having a specified partial order",
      "tags": [
        "common-gender"
      ],
      "word": "partiellt ordnad mängd"
    }
  ],
  "wikipedia": [
    "partially ordered set"
  ],
  "word": "partially ordered set"
}

Download raw JSONL data for partially ordered set meaning in English (4.8kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.