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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Every $ {\rm low}\sb 2$ Boolean algebra has a recursive copy


Author: John J. Thurber
Journal: Proc. Amer. Math. Soc. 123 (1995), 3859-3866
MSC: Primary 03C57; Secondary 03D30, 03D45, 03D80
MathSciNet review: 1283564
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Abstract: The degree of a structure $ \mathcal{A}$ is the Turing degree of its open diagram $ D(\mathcal{A})$, coded as a subset of $ \omega $. Implicit in the definition is a particular presentation of the structure; the degree is not an isomorphism invariant. We prove that if a Boolean algebra $ \mathcal{A}$ has a copy of $ {\text{low}_2}$ degree, then there is a recursive Boolean algebra $ \mathcal{B}$ which is isomorphic to $ \mathcal{A}$. This builds on work of Downey and Jockusch, who proved the analogous result starting with a $ {\text{low}_1}$ Boolean algebra.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283564-6
PII: S 0002-9939(1995)1283564-6
Article copyright: © Copyright 1995 American Mathematical Society