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Descriptive Set Theory and Computable Topology (Dagstuhl Seminar 21461)

Authors Mathieu Hoyrup, Arno Pauly, Victor Selivanov, Mariya I. Soskova and all authors of the abstracts in this report



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Author Details

Mathieu Hoyrup
  • LORIA & INRIA Nancy, FR
Arno Pauly
  • Swansea University, GB
Victor Selivanov
  • A. P. Ershov Institute - Novosibirsk, RU
Mariya I. Soskova
  • University of Wisconsin - Madison, US
and all authors of the abstracts in this report

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Mathieu Hoyrup, Arno Pauly, Victor Selivanov, and Mariya I. Soskova. Descriptive Set Theory and Computable Topology (Dagstuhl Seminar 21461). In Dagstuhl Reports, Volume 11, Issue 10, pp. 72-93, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/DagRep.11.10.72

Abstract

Computability and continuity are closely linked - in fact, continuity can be seen as computability relative to an arbitrary oracle. As such, concepts from topology and descriptive set theory feature heavily in the foundations of computable analysis. Conversely, techniques developed in computability theory can be fruitfully employed in topology and descriptive set theory, even if the desired results mention no computability at all. In this Dagstuhl Seminar, we brought together researchers from computable analysis, from classical computability theory, from descriptive set theory, formal topology, and other relevant areas. Our goals were to identify key open questions related to this interplay, to exploit synergies between the areas and to intensify collaboration between the relevant communities.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computability
  • Theory of computation → Logic
  • Mathematics of computing → Topology
Keywords
  • computable analysis
  • enumeration degrees
  • quasi-polish spaces
  • synthetic topology

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