Every 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 is the Turing degree of its open diagram , coded as a subset of . 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 has a copy of degree, then there is a recursive Boolean algebra which is isomorphic to . This builds on work of Downey and Jockusch, who proved the analogous result starting with a Boolean algebra.

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1283564-6

Article copyright:
© Copyright 1995
American Mathematical Society