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<p>This paper investigates non-extensional control structures such as effective composition, s-m-n theorem, Kleene’s recursion theorem, among others, in computable numberings of families of partial recursive functions and their invariance under the completion operator. Additionally, we introduce a method for constructing complete non-principal numberings, which is then used to analyze the effectivity degrees of control structures in universal complete numberings.</p>

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Control Structures in Computable Numberings and the Completion Operator

  • 期刊论文

  • 发表日期：

    2025年4月26日

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  • Marat Faizrahmanov

摘要

This paper investigates non-extensional control structures such as effective composition, s-m-n theorem, Kleene’s recursion theorem, among others, in computable numberings of families of partial recursive functions and their invariance under the completion operator. Additionally, we introduce a method for constructing complete non-principal numberings, which is then used to analyze the effectivity degrees of control structures in universal complete numberings.