The \(\Delta_2^0\)-spectrum of a linear order (Q2747698)
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scientific article; zbMATH DE number 1658156
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\Delta_2^0\)-spectrum of a linear order |
scientific article; zbMATH DE number 1658156 |
Statements
5 September 2002
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spectrum
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linear order
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structures
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Turing degrees
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The \(\Delta_2^0\)-spectrum of a linear order (English)
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The spectrum \(\text{Spec}(S)\) of an algebraic structure \(S\) is the class of Turing degrees of presentations of \(S\). Slaman and independently Wehner constructed an example of a structure with \(\text{Spec}(S)= {\mathbf D}\setminus \{\mathbf{0}\}\) where \textbf{D} is the class of all Turing degrees. Answering a question of Downey, the author constructs an example of a linear order whose spectrum includes every non-computable \(\Delta_2^0\)-degree.
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