See subuppersemilattice on Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "sub", "3": "uppersemilattice" }, "expansion": "sub- + uppersemilattice", "name": "prefix" } ], "etymology_text": "From sub- + uppersemilattice.", "forms": [ { "form": "subuppersemilattices", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "subuppersemilattice (plural subuppersemilattices)", "name": "en-noun" } ], "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" }, { "kind": "other", "name": "English terms prefixed with sub-", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "1988, Manuel Lerman, Richard A. Shore-, “Decidability and invariant classes for degree structures”, in Transactions of the American Mathematical Society, volume 310, number 2:", "text": "First, given any finite subuppersemilattice U ot 3[0,0'] with top element 0' and an isomorphism type V of a poset extending U consistently with its structure as an usl such that V and U have the same top element and V is an end extension of ...", "type": "quote" }, { "ref": "2016, James Barnes, “On the decidability of the Σ₂ theories of the arithmetic and hyperarithmetic degrees as uppersemilattices”, in arXiv:", "text": "This is achieved by using Kumabe-Slaman forcing - along with other known results - to show that given finite uppersemilattices #x5C;mathcal#x7B;M#x7D; and #x5C;mathcal#x7B;N#x7D;, where #x5C;mathcal#x7B;M#x7D; is a subuppersemilattice of #x5C;mathcal#x7B;N#x7D;, then for both degree structures, every embedding of #x5C;mathcal#x7B;M#x7D; into the structure extends to one of #x5C;mathcal#x7B;N#x7D; iff #x5C;mathcal#x7B;N#x7D; is an end-extension of #x5C;mathcal#x7B;M#x7D;..", "type": "quote" } ], "glosses": [ "A sub-semilattice of an uppersemilattice." ], "id": "en-subuppersemilattice-en-noun-ZnqLl0LS", "links": [ [ "mathematics", "mathematics" ] ], "raw_glosses": [ "(mathematics) A sub-semilattice of an uppersemilattice." ], "topics": [ "mathematics", "sciences" ] } ], "word": "subuppersemilattice" }
{ "etymology_templates": [ { "args": { "1": "en", "2": "sub", "3": "uppersemilattice" }, "expansion": "sub- + uppersemilattice", "name": "prefix" } ], "etymology_text": "From sub- + uppersemilattice.", "forms": [ { "form": "subuppersemilattices", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "subuppersemilattice (plural subuppersemilattices)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms prefixed with sub-", "English terms with quotations", "Pages with 1 entry", "Pages with entries", "en:Mathematics" ], "examples": [ { "ref": "1988, Manuel Lerman, Richard A. Shore-, “Decidability and invariant classes for degree structures”, in Transactions of the American Mathematical Society, volume 310, number 2:", "text": "First, given any finite subuppersemilattice U ot 3[0,0'] with top element 0' and an isomorphism type V of a poset extending U consistently with its structure as an usl such that V and U have the same top element and V is an end extension of ...", "type": "quote" }, { "ref": "2016, James Barnes, “On the decidability of the Σ₂ theories of the arithmetic and hyperarithmetic degrees as uppersemilattices”, in arXiv:", "text": "This is achieved by using Kumabe-Slaman forcing - along with other known results - to show that given finite uppersemilattices #x5C;mathcal#x7B;M#x7D; and #x5C;mathcal#x7B;N#x7D;, where #x5C;mathcal#x7B;M#x7D; is a subuppersemilattice of #x5C;mathcal#x7B;N#x7D;, then for both degree structures, every embedding of #x5C;mathcal#x7B;M#x7D; into the structure extends to one of #x5C;mathcal#x7B;N#x7D; iff #x5C;mathcal#x7B;N#x7D; is an end-extension of #x5C;mathcal#x7B;M#x7D;..", "type": "quote" } ], "glosses": [ "A sub-semilattice of an uppersemilattice." ], "links": [ [ "mathematics", "mathematics" ] ], "raw_glosses": [ "(mathematics) A sub-semilattice of an uppersemilattice." ], "topics": [ "mathematics", "sciences" ] } ], "word": "subuppersemilattice" }
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