发表机构
University of Camerino（卡梅里诺大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明每个非递归多一度要么含一个有限一度要么含无穷多个有限一度，否定了Richter等人的开放问题2，填补了该问题对所有非递归多一度的结论空白。
AI 中文摘要
本文证明，每个非递归多一度恰好包含一个有限一度，或无穷多个有限一度。这否定了Richter、Stephan和Zhang的开放问题2。早期研究表明，对于2^N上标准乘积测度下几乎所有自然数子集A，其度[A]_m包含有限一度的无穷反链，该问题已获得几乎必然否定的答案；本文定理则为每个非递归多一度解决了该问题。
英文摘要
This paper proves that every nonrecursive many-one degree contains either exactly one or infinitely many finite-one degrees. This gives a negative answer to Open Question 2 of Richter, Stephan, and Zhang~\cite[p.~17]{RSZ}. Earlier work established that, for almost every $A\subseteq\N$ with respect to the standard product measure on $2^\N$, the degree $[A]_{\m}$ contains an infinite antichain of finite-one degrees~\cite{Cintioli}. Thus the question had already received an almost-sure negative answer; the present theorem settles it for every nonrecursive many-one degree.
Comments15 pages
