Work

Computable Closed Euclidean Subsets with and without Computable Points

Year: 2006

Type: preprint

Abstract: The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are `large' in the sense of positive Lebesgue measure. We observe that a certain size is in fact necessary: every non-empty co-r.e. closed real set without computable points has continuum cardinality. This leads us to investigate for various classes of computable real subsets whether they necessarily contain a (not necessarily effectively findable) computable point.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.cs/0610080

Authors: Roux, Stéphane Le, Ziegler, Martin

Institutions: Japan Advanced Institute of Science and Technology, Paderborn University

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Ministère des Affaires Etrangères, Ministère de l'Enseignement Supérieur et de la Recherche, Japan Society for the Promotion of Science

Award: G8042849476

OpenAlex ID: W4298880847

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