A closed subset of Baire space not Medvedev equivalent to any closed set of Cantor space

IF 0.5 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2025-04-25 DOI:10.1007/s00153-025-00973-6

Joshua A. Cole

引用次数: 0

Abstract

For mass problems \(P,Q\subseteq {\mathbb {N}^\mathbb {N}}\) (Baire space), P is Medvedev reducible to Q (\(P\le _sQ\)) if for some Turing funcional \(\Phi \), \(\Phi (Q)\subseteq P\), and Medvedev equivalent to Q if also \(Q\le _sP\). Shafer asked if every closed problem P is Medvedev equivalent to a closed problem Q with \(Q\subseteq 2^\mathbb {N}\) (Cantor space). We show that this is not the case.

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非Medvedev的Baire空间的闭子集等价于任何Cantor空间的闭集

对于质量问题\(P,Q\subseteq {\mathbb {N}^\mathbb {N}}\)（贝尔空间），如果对于某些图灵泛函\(\Phi \), \(\Phi (Q)\subseteq P\)， P是梅德韦杰夫可约为Q (\(P\le _sQ\))，并且梅德韦杰夫等价于Q，如果也是\(Q\le _sP\)。Shafer问是否每个封闭问题P都是梅德韦杰夫等价于具有\(Q\subseteq 2^\mathbb {N}\) （Cantor空间）的封闭问题Q。我们证明事实并非如此。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.