See arithmetical hierarchy on Wiktionary
{ "forms": [ { "form": "arithmetical hierarchies", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "arithmetical hierarchy (plural arithmetical hierarchies)", "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": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Logic", "orig": "en:Logic", "parents": [ "Formal sciences", "Philosophy", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers." ], "id": "en-arithmetical_hierarchy-en-noun-6QYaUK9j", "links": [ [ "logic", "logic" ], [ "hierarchy", "hierarchy" ], [ "classifies", "classify" ], [ "complexity", "complexity" ], [ "first-order", "first-order" ], [ "formula", "formula" ], [ "set", "set" ], [ "alternation", "alternation" ], [ "series", "series" ], [ "unbounded", "unbounded" ], [ "existential quantifier", "existential quantifier" ], [ "universal quantifier", "universal quantifier" ] ], "raw_glosses": [ "(logic) A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers." ], "synonyms": [ { "word": "arithmetic hierarchy" }, { "word": "Kleene hierarchy" }, { "word": "Kleene-Mostowski hierarchy" } ], "topics": [ "human-sciences", "logic", "mathematics", "philosophy", "sciences" ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "Translations", "word": "aritmeettinen hierarkia" }, { "code": "de", "lang": "German", "sense": "Translations", "tags": [ "feminine" ], "word": "arithmetische Hierarchie" }, { "code": "pl", "lang": "Polish", "sense": "Translations", "tags": [ "feminine" ], "word": "hierarchia arytmetyczna" } ], "wikipedia": [ "arithmetical hierarchy" ] } ], "word": "arithmetical hierarchy" }
{ "forms": [ { "form": "arithmetical hierarchies", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "arithmetical hierarchy (plural arithmetical hierarchies)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "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 Finnish translations", "Terms with German translations", "Terms with Polish translations", "Translation table header lacks gloss", "en:Logic" ], "glosses": [ "A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers." ], "links": [ [ "logic", "logic" ], [ "hierarchy", "hierarchy" ], [ "classifies", "classify" ], [ "complexity", "complexity" ], [ "first-order", "first-order" ], [ "formula", "formula" ], [ "set", "set" ], [ "alternation", "alternation" ], [ "series", "series" ], [ "unbounded", "unbounded" ], [ "existential quantifier", "existential quantifier" ], [ "universal quantifier", "universal quantifier" ] ], "raw_glosses": [ "(logic) A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers." ], "topics": [ "human-sciences", "logic", "mathematics", "philosophy", "sciences" ], "wikipedia": [ "arithmetical hierarchy" ] } ], "synonyms": [ { "word": "arithmetic hierarchy" }, { "word": "Kleene hierarchy" }, { "word": "Kleene-Mostowski hierarchy" } ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "Translations", "word": "aritmeettinen hierarkia" }, { "code": "de", "lang": "German", "sense": "Translations", "tags": [ "feminine" ], "word": "arithmetische Hierarchie" }, { "code": "pl", "lang": "Polish", "sense": "Translations", "tags": [ "feminine" ], "word": "hierarchia arytmetyczna" } ], "word": "arithmetical hierarchy" }
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This page is a part of the kaikki.org machine-readable All languages combined 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.
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