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<p>We consider the uniformity of constructions in computability theory. Examples of uniform and nonuniform constructions in Turing degree theory are considered, including the completeness criterion for computably enumerable sets, the Sacks Jump Theorem, constructions of effectively nowhere simple sets, and the problem of uniformly obtaining a computably enumerable set below an arbitrary 2-computably enumerable set. Results by Arslanov, Yamaleev, Downey, Stob, Terwijn, and others are analyzed. Open questions on Σ<sub>1</sub>-embeddability of structures of n-computably enumerable degrees are discussed.</p>

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Uniform Constructions in Computability Theory

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • M. M. Arslanov

摘要

We consider the uniformity of constructions in computability theory. Examples of uniform and nonuniform constructions in Turing degree theory are considered, including the completeness criterion for computably enumerable sets, the Sacks Jump Theorem, constructions of effectively nowhere simple sets, and the problem of uniformly obtaining a computably enumerable set below an arbitrary 2-computably enumerable set. Results by Arslanov, Yamaleev, Downey, Stob, Terwijn, and others are analyzed. Open questions on Σ1-embeddability of structures of n-computably enumerable degrees are discussed.