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]
^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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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...
determined. The converse does not hold; however, if every game in a given adequatepointclass Γ {\displaystyle \Gamma } is determined, then every set in Γ {\displaystyle...
} If Γ {\displaystyle {\boldsymbol {\Gamma }}} is an adequatepointclass whose dual pointclass has the prewellordering property, then Γ {\displaystyle...
close: A simple modification of the argument shows that if Γ is an adequatepointclass such that every game in Γ is determined, then every set of reals...
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