Automorphisms of the lattice of \(\Pi_1^0\) classes; perfect thin classes and anc degrees (Q2750927)
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scientific article; zbMATH DE number 1663170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Automorphisms of the lattice of \(\Pi_1^0\) classes; perfect thin classes and anc degrees |
scientific article; zbMATH DE number 1663170 |
Statements
21 October 2001
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thin class
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automorphisms
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invariance
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Automorphisms of the lattice of \(\Pi_1^0\) classes; perfect thin classes and anc degrees (English)
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The paper is devoted to the study of the lattice of \(\Pi_{1}^{0}\) classes. It focuses on the analog of maximality, or, more precisely, hyperhypersimplicity, namely the notion of a thin class. A number of results relating automorphisms, invariance and thin classes is proved. The main results are an analog of Martin's work on hyperhypersimple sets and high degrees and an analog of Soare's work demonstrating that maximal sets form an orbit.
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