RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Sibirsk. Mat. Zh., 2005, Volume 46, Number 4, Pages 928–941 (Mi smj1015)

The degree spectra of definable relations on Boolean algebras

P. M. Semukhin

Novosibirsk State University, Mechanics and Mathematics Department

Abstract: We study some questions concerning the structure of the spectra of the sets of atoms and atomless elements in a computable Boolean algebra. We prove that if the spectrum of the set of atoms contains a 1-low degree then it contains a computable degree. We show also that in a computable Boolean algebra of characteristic $(1,1,0)$ whose set of atoms is computable the spectrum of the atomless ideal consists of all $\Pi_2^0$ degrees.

Keywords: Boolean algebras, computable models, spectra of relations

Full text: PDF file (255 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2005, 46:4, 740–750

Bibliographic databases:

UDC: 510.5, 512.563
Revised: 27.04.2005

Citation: P. M. Semukhin, “The degree spectra of definable relations on Boolean algebras”, Sibirsk. Mat. Zh., 46:4 (2005), 928–941; Siberian Math. J., 46:4 (2005), 740–750

Citation in format AMSBIB
\Bibitem{Sem05} \by P.~M.~Semukhin \paper The degree spectra of definable relations on Boolean algebras \jour Sibirsk. Mat. Zh. \yr 2005 \vol 46 \issue 4 \pages 928--941 \mathnet{http://mi.mathnet.ru/smj1015} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2169408} \zmath{https://zbmath.org/?q=an:1119.03042} \transl \jour Siberian Math. J. \yr 2005 \vol 46 \issue 4 \pages 740--750 \crossref{https://doi.org/10.1007/s11202-005-0074-2} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000231331700017} 

• http://mi.mathnet.ru/eng/smj1015
• http://mi.mathnet.ru/eng/smj/v46/i4/p928

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. A. Bazhenov, “Degrees of categoricity for superatomic Boolean algebras”, Algebra and Logic, 52:3 (2013), 179–187
2. N. A. Bazhenov, “Boolean algebras with distinguished endomorphisms and generating trees”, J. Math. Sci., 215:4 (2016), 460–474
•  Number of views: This page: 164 Full text: 48 References: 38