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<p>We generalize the concept of an&#xa0;effectively minimal numberingobtained by its relativizationwith respect to the Turing jumps of subsets of nonnegative integers.Basing on this generalization,we&#xa0;classify the minimal numberingscomputable in the arithmetical and hyperarithmetical hierarchies.</p>

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An Approach to the Classification of Minimal Numberings of Families of Arithmetical Sets

  • 期刊论文

  • 发表日期：

    2025年3月23日

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  • M. Kh. Faizrahmanov

摘要

We generalize the concept of an effectively minimal numberingobtained by its relativizationwith respect to the Turing jumps of subsets of nonnegative integers.Basing on this generalization,we classify the minimal numberingscomputable in the arithmetical and hyperarithmetical hierarchies.