不动点与相对预完全性
Fixpoints and relative precompleteness
摘要：
我们在数论的背景下研究相对预完全性，并将其与低度的概念联系起来。我们引入了数的整除性的概念，并用它来表明，对于可整除数类，低和相对预完全性与可计算性相一致。我们还研究了Skolem函数的复杂性所产生的Arslanov的完整性准则与参数。我们表明，适当整除的号码，这些Skolem功能具有最大可能的图灵度。特别是，这适用于部分可计算函数的标准编号和c.e.集.
英文摘要：
We study relative precompleteness in the context of the theory of numberings, and relate this to a notion of lowness. We introduce a notion of divisibility for numberings, and use it to show that for the class of divisible numberings, lowness and relative precompleteness coincide with being computable. We also study the complexity of Skolem functions arising from Arslanov's completeness criterion with parameters. We show that for suitably divisible numberings, these Skolem functions have the maximal possible Turing degree. In particular this holds for the standard numberings of the partial computable functions and the c.e. sets.
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