The Ershov hierarchy (Q2906563)
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scientific article; zbMATH DE number 6077600
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Ershov hierarchy |
scientific article; zbMATH DE number 6077600 |
Statements
5 September 2012
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Ershov hierarchy
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difference hierarchy
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\(n\)-c.e. sets
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\(\Delta_2^0\) sets
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tutorial
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The Ershov hierarchy (English)
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A nice tutorial on the Ershov difference hierarchy, tracing the field from its roots about fifty years ago up through current developments. The first half of the paper presents the hierarchy of \(n\)-c.e. sets, independently due to Gold and Putnam in 1965, along with Ershov's extension of that hierarchy to transfinite levels. Besides many results due to Ershov, contributions of Epstein, Hass, and Kramer, and of Faizrahmanov are also discussed. The paper's second half focuses on the \(n\)-c.e. Turing degrees, covering results of Cooper, the author, and several others. Connections with the \(n\)-CEA hierarchy are also examined. The survey concludes with various open questions and conjectures.NEWLINENEWLINEFor the entire collection see [Zbl 1235.03005].
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