论文标题
同构紧凑型波兰空间的同态类型的学位光谱
Degree spectra of homeomorphism types of compact Polish spaces
论文作者
论文摘要
波兰空间并不总是对可计算的波兰空间的同构。在本文中，我们研究了呈现紧凑型波兰空间的同构副本的非竞争性程度。我们表明，存在$ 0'$ - 可计算的低$ _3 $紧凑型波兰空间，这对一个可计算的空间不是同型的，并且对于任何自然数量$ n \ geq 2 $，都存在波兰空间$ x_n $，因此需要高$ _ {n} $ - degrees呈现$ x_n $ $ x_n $。我们还表明，关于图灵的降低性，没有紧凑的抛光空间最少。 本文的第一个版本出现在2020年4月。2023年9月进行了重大更新，并改进了证明和结果。这是从2024年1月开始的最终版本，对čech同源性小组的结果有更多结果。
A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $0'$-computable low$_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high$_{n}$-degrees are required to present the homeomorphism type of $X_n$. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. The first version of this article appeared in April 2020. A major update was made in September 2023, with improved proofs and results. This is the final version from January 2024, with more results on Čech homology groups.
