Sibirskii Matematicheskii Zhurnal
 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., 2006, Volume 47, Number 3, Pages 695–706 (Mi smj887)

On $\Sigma$-subsets of naturals over abelian groups

A. N. Khisamiev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We obtain conditions for the $\Sigma$-definability of a subset of the set of naturals in the hereditarily finite admissible set over a model and for the computability of a family of such subsets. We prove that: for each $e$-ideal $I$ there exists a torsion-free abelian group $A$ such that the family of $e$-degrees of $\Sigma$-subsets of $\omega$ in $\mathbb{HF}(A)$ coincides with $I$ there exists a completely reducible torsion-free abelian group in the hereditarily finite admissible set over which there exists no universal $\Sigma$-function; for each principal $e$-ideal $I$ there exists a periodic abelian group $A$ such that the family of $e$-degrees of $\Sigma$-subsets of $\omega$ in $\mathbb{HF}(A)$ coincides with $I$.

Keywords: admissible set, e-reducibility, computability, $\Sigma$-definability, abelian group

Full text: PDF file (248 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2006, 47:3, 574–583

Bibliographic databases:

UDC: 512.540, 510.5

Citation: A. N. Khisamiev, “On $\Sigma$-subsets of naturals over abelian groups”, Sibirsk. Mat. Zh., 47:3 (2006), 695–706; Siberian Math. J., 47:3 (2006), 574–583

Citation in format AMSBIB
\Bibitem{Khi06} \by A.~N.~Khisamiev \paper On $\Sigma$-subsets of naturals over abelian groups \jour Sibirsk. Mat. Zh. \yr 2006 \vol 47 \issue 3 \pages 695--706 \mathnet{http://mi.mathnet.ru/smj887} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2251077} \zmath{https://zbmath.org/?q=an:1115.03038} \transl \jour Siberian Math. J. \yr 2006 \vol 47 \issue 3 \pages 574--583 \crossref{https://doi.org/10.1007/s11202-006-0068-8} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000239228700017} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33744721349} 

• http://mi.mathnet.ru/eng/smj887
• http://mi.mathnet.ru/eng/smj/v47/i3/p695

 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. A. N. Khisamiev, “On quasiresolvent periodic abelian groups”, Siberian Math. J., 48:6 (2007), 1115–1126
2. A. N. Khisamiev, “$\Sigma$-Bounded algebraic systems and universal functions. I”, Siberian Math. J., 51:1 (2010), 178–192
3. Khisamiev A.N., “Bounded algebraic systems and universal functions”, Doklady Mathematics, 81:2 (2010), 309–311
4. A. N. Khisamiev, “$\Sigma$-uniform structures and $\Sigma$-functions. I”, Algebra and Logic, 50:5 (2011), 447–465
5. A. N. Khisamiev, “On a universal $\Sigma$-function over a tree”, Siberian Math. J., 53:3 (2012), 551–553
6. A. N. Khisamiev, “Universal functions and almost $c$-simple models”, Siberian Math. J., 56:3 (2015), 526–540
7. A. N. Khisamiev, “Universal functions over trees”, Algebra and Logic, 54:2 (2015), 188–193
8. A. N. Khisamiev, “A class of almost $c$-simple rings”, Siberian Math. J., 56:6 (2015), 1133–1141
9. A. N. Khisamiev, “Universal functions and unbounded branching trees”, Algebra and Logic, 57:4 (2018), 309–319
10. A. N. Khisamiev, “Universalnye funktsii i $K\Sigma$-struktury”, Sib. matem. zhurn., 61:3 (2020), 703–716
•  Number of views: This page: 265 Full text: 80 References: 51

 Contact us: math-net2021_11 [at] mi-ras ru Terms of Use Registration to the website Logotypes © Steklov Mathematical Institute RAS, 2021