# Adequate pointclass
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In the mathematical field of [descriptive set theory](/source/descriptive_set_theory), a '''[pointclass](/source/pointclass)''' can be called '''adequate''' if it contains all [recursive](/source/Recursive_set) pointsets and is closed under recursive substitution, [bounded](/source/bounded_quantifier) universal and existential quantification and preimages by recursive functions.[{{citation|title=Descriptive Set Theory|series=Studies in Logic and the Foundations of Mathematics|first=Y. N.|last=Moschovakis|publisher=Elsevier|year=1987|isbn=9780080963198|page=158|url=https://books.google.com/books?id=c7FQWlkA3KIC&pg=PA158}}.][{{citation|title=Sets and Extensions in the Twentieth Century|volume=6|series=Handbook of the History of Logic|first1=Dov M.|last1=Gabbay|first2=Akihiro|last2=Kanamori|first3=John|last3=Woods|publisher=Elsevier|year=2012|isbn=9780080930664|page=465|url=https://books.google.com/books?id=RBrWwKVbmMUC&pg=PA465}}.] This ensures that an adequate pointclass is robust enough to include computable sets and remain stable under fundamental operations, making it a key tool for studying the complexity and definability of sets in effective descriptive set theory.
==References==
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Category:Descriptive set theory
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