Index sets for classes
نویسنده
چکیده
A class is an e ectively closed set of reals We study properties of these classes determined by cardinality measure and category as well as by the complexity of the members of a class P Given an e ective enumeration fPe e g of the classes the index set I for a certain property such as having positive measure is the set of indices e such that Pe has the property For example the index set of binary classes of positive measure is complete Various notions of boundedness including a new notion of almost bounded classes are discussed and classi ed For example the index set of the recursively bounded classes is complete and the index set of the recursively bounded classes which have in nitely many recursive members is complete Consideration of the Cantor Bendixson derivative leads to index sets in the trans nite levels of the hyperarithmetic hierarchy
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