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Adequate pointclass
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<p>In the mathematical field of <a href="/facts/Descriptive_set_theory/ek0tvUXb">descriptive set theory</a>, a <a href="/facts/Pointclass/k6fMNJa7">pointclass</a> can be called adequate if it contains all <a href="/facts/Recursive_set/rsnT9cLn">recursive</a> pointsets and is closed under recursive substitution, <a href="/facts/Bounded_quantifier/Q0Y7aTkG">bounded</a> universal and existential quantification and preimages by recursive functions. 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. </p>