See Löwenheim-Skolem theorem on Wiktionary
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{ "etymology_text": "Named for Leopold Löwenheim and Thoralf Skolem.", "head_templates": [ { "args": {}, "expansion": "Löwenheim-Skolem theorem", "name": "en-proper noun" } ], "lang": "English", "lang_code": "en", "pos": "name", "senses": [ { "categories": [ "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English proper nouns", "English terms spelled with Ö", "English terms spelled with ◌̈", "English uncountable nouns", "Pages with 1 entry", "Pages with entries" ], "glosses": [ "A theorem stating that, if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism." ], "links": [ [ "countable", "countable" ], [ "first-order", "first-order" ], [ "theory", "theory" ], [ "infinite", "infinite" ], [ "model", "model" ], [ "cardinal number", "cardinal number" ], [ "isomorphism", "isomorphism" ] ], "qualifier": "mathematical logic", "raw_glosses": [ "(mathematical logic) A theorem stating that, if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism." ], "wikipedia": [ "Löwenheim-Skolem theorem" ] } ], "word": "Löwenheim-Skolem theorem" }
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