Isomorphism of Computable Structures and Vaught's Conjecture
Howard Becker · Journal of Symbolic Logic · 2013
Abstract The following question is open: Does there exist a hyperarithmetic class of computable structures with exactly one non-hyperarithmetic isomorphism-type? Given any oracle α ∈ 2ω, we can ask the same question relativized to α. A negative answer for every α implies Vaught's Conjecture for Lω1ω.