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Isomorphism of computable structures and Vaught’s conjecture. (English) Zbl 1349.03035
Summary: The following question is open: Does there exist a hyperarithmetic class of computable structures with exactly one non-hyperarithmetic isomorphism-type? Given any oracle $$a \in 2^\omega$$, we can ask the same question relativized to $$a$$. A negative answer for every $$a$$ implies Vaught’s Conjecture for $$L_{\omega_1 \omega}$$.

##### MSC:
 03C57 Computable structure theory, computable model theory 03D45 Theory of numerations, effectively presented structures 03E15 Descriptive set theory
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