Oracle with $\mathrm{P}=\mathrm{NP}\cap \mathrm{coNP}$, but no Many-One Completeness in UP, DisjNP, and DisjCoNP

Anton Ehrmanntraut, Fabian Egidy, Christian Glaßer

We construct an oracle relative to which $\mathrm{P}=\mathrm{NP}\cap \mathrm{coNP}$, but there are no many-one complete sets in $\mathrm{UP}$, no many-one complete disjoint $\ma…