Assuming AD + DC(R), we characterize the self-dual boldface pointclasses which are strictly larger (in terms of cardinality) than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank " !! 1, and those of Wadge rank < !! 1 when " is limit.
Effective Cardinals of Boldface Pointclasses
ANDRETTA, Alessandro;
2007-01-01
Abstract
Assuming AD + DC(R), we characterize the self-dual boldface pointclasses which are strictly larger (in terms of cardinality) than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank " !! 1, and those of Wadge rank < !! 1 when " is limit.
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