Journal of Symbolic Logic

Isomorphism of computable structures and Vaught's Conjecture

Howard Becker

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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 $L_{\omega_1 \omega}$.

Article information

J. Symbolic Logic, Volume 78, Issue 4 (2013), 1328-1344.

First available in Project Euclid: 5 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C57: Effective and recursion-theoretic model theory [See also 03D45] 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55] 03E15: Descriptive set theory [See also 28A05, 54H05]


Becker, Howard. Isomorphism of computable structures and Vaught's Conjecture. J. Symbolic Logic 78 (2013), no. 4, 1328--1344. doi:10.2178/jsl.7804180.

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