Relative to any non-hyperarithmetic set (Q2853977)
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scientific article; zbMATH DE number 6215936
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Relative to any non-hyperarithmetic set |
scientific article; zbMATH DE number 6215936 |
Statements
17 October 2013
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hyperarithmetic
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degree spectrum
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computable structure
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Relative to any non-hyperarithmetic set (English)
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The degree spectrum of a countable structure \(M\) is defined as the collection of all Turing degrees which compute an isomorphic copy of \(M\) whose universe is the subset of the set of natural numbers.NEWLINENEWLINEThe main results of the paper are the following statements: 1) there is a countable linear ordering whose degree spectrum consists of the non-hyperarithmetic degrees; 2) there is a structure whose degree spectrum is null and co-meager; 3) there is a structure whose degree spectrum is meager and co-null.
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