Degree Spectra of Homeomorphism Types of Compact Polish Spaces - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... 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. This version is a major update from September 2023, with improved proofs and results.
Fichier principal
Vignette du fichier
article.pdf (418.51 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)

Licence

Attribution

Identifiers

  • HAL Id : hal-02555111 , version 2

Cite

Mathieu Hoyrup, Takayuki Kihara, Victor Selivanov. Degree Spectra of Homeomorphism Types of Compact Polish Spaces. 2023. ⟨hal-02555111v2⟩
92 View
45 Download

Share

Gmail Facebook X LinkedIn More