Every recursive Boolean algebra is isomorphic to one with incomplete atoms (Q1210349)
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scientific article; zbMATH DE number 179073
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Every recursive Boolean algebra is isomorphic to one with incomplete atoms |
scientific article; zbMATH DE number 179073 |
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Every recursive Boolean algebra is isomorphic to one with incomplete atoms (English)
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11 August 1993
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It is shown that for any recursive Boolean algebra \(B_ 0\) there is a recursive Boolean algebra \(B_ 1\) isomorphic to \(B_ 0\) such that the atoms of \(B_ 1\) are Turing incomplete. The proof is a sophisticated blend of an algebraic technique of Remmel and Vaught with a tree of strategies argument. The result constitutes the solution to an old question of Remmel.
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degrees of undecidability
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recursive Boolean algebra
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Turing incomplete
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