Degree Spectra of Homeomorphism Types of Compact Polish Spaces - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles The Journal of Symbolic Logic Year : 2023

Degree Spectra of Homeomorphism Types of Compact Polish Spaces

Abstract

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.
Fichier principal
Vignette du fichier
final.pdf (479.06 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02555111 , version 1 (27-04-2020)
hal-02555111 , version 2 (18-09-2023)
hal-02555111 , version 3 (02-01-2024)

Licence

Identifiers

Cite

Mathieu Hoyrup, Takayuki Kihara, Victor Selivanov. Degree Spectra of Homeomorphism Types of Compact Polish Spaces. The Journal of Symbolic Logic, In press, pp.1-32. ⟨10.1017/jsl.2023.93⟩. ⟨hal-02555111v3⟩
165 View
99 Download

Altmetric

Share

More