The isomorphism conjecture holds relative to an oracle

The authors introduce symmetric perfect generic sets. these sets vary from the usual generic sets by allowing limited infinite encoding into the oracle. They then show that the Berman-Hartmanis (1977) isomorphism conjecture holds relative to any sp-generic oracle, i.e., for any symmetric perfect generic set A, all NP^A -complete sets are polynomial-time isomorphic relative to A . As part of the proof that the isomorphism conjecture holds relative to symmetric perfect generic sets they also show that P^A=FewP^A for any symmetric perfect generic^A