Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Bazhenov, Nikolay; *; †
Affiliations: Sobolev Institute of Mathematics, Novosibirsk, Russia and Novosibirsk State University, Novosibirsk, Russia. bazhenov@math.nsc.ru
Correspondence: [*] Address for correspondence: Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090, Novosibirsk, Russia.
Note: [*] The author was partially supported by the grant of the President of the Russian Federation (No. MK-1214.2019.1). The author is grateful to Sergey Goncharov and Stanislav Speranski for helpful discussions.
Abstract: We investigate computability-theoretic properties of contact algebras. These structures were introduced by Dimov and Vakarelov in [Fundam. Inform. 74 (2006), 209–249] as an axiomatization for the region-based theory of space. We prove that the class of countable contact algebras is complete with respect to degree spectra of nontrivial structures, effective dimensions, expansion by constants, and degree spectra of relations. This means that the class of contact algebras is very rich from the computability-theoretic point of view. As an application of our result, we show that the ∏3-theory of contact algebras is hereditarily undecidable. This is a refinement of the result of Koppelberg, Düntsch, and Winter [Algebra Univers., 68 (2012), 353–366].
Keywords: Contact algebra, computable structure, Boolean algebra, degree spectrum, computable dimension, contact relation, region-based theory of space, elementary definability, hereditary undecidability
DOI: 10.3233/FI-2019-1817
Journal: Fundamenta Informaticae, vol. 167, no. 4, pp. 257-269, 2019
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
sales@iospress.com
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
info@iospress.nl
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office info@iospress.nl
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
china@iospress.cn
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
如果您在出版方面需要帮助或有任何建, 件至: editorial@iospress.nl