Adequate pointclass

In the mathematical field of descriptive set theory, a pointclass can be called adequate if it contains all recursive pointsets and is closed under recursive substitution, bounded universal and existential quantification and preimages by recursive functions.^[1]^[2] 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

^ Moschovakis, Y. N. (1987), Descriptive Set Theory, Studies in Logic and the Foundations of Mathematics, Elsevier, p. 158, ISBN 9780080963198.
^ Gabbay, Dov M.; Kanamori, Akihiro; Woods, John (2012), Sets and Extensions in the Twentieth Century, Handbook of the History of Logic, vol. 6, Elsevier, p. 465, ISBN 9780080930664.

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[1] Moschovakis, Y. N. (1987), Descriptive Set Theory, Studies in Logic and the Foundations of Mathematics, Elsevier, p. 158, ISBN 9780080963198.

[2] Gabbay, Dov M.; Kanamori, Akihiro; Woods, John (2012), Sets and Extensions in the Twentieth Century, Handbook of the History of Logic, vol. 6, Elsevier, p. 465, ISBN 9780080930664.

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