**Authors:** Richard Beigel, Harry Buhrman, and Lance Fortnow

**Abstract:**
We construct an oracle *A* such that

- The oracle
*A*gives the first relativized world where one can solve satisfiability on formulae with at most one assignment yet P ≠ NP. - The oracle
*A*is the first whereP ^{A}= UP^{A}≠ NP^{A}= co-NP^{A}. - The construction gives a much simpler proof than that of Fenner, Fortnow and Kurtz of a relativized world where all the NP-complete sets are polynomial-time isomorphic. It is the first such computable oracle.
- Relative to
*A*we have a collapse of PARITYEXP^{A}⊆ ZPP^{A}⊆ P^{A}/poly.