Algebra i Logika. Seminar
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



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Logika. Sem., 1967, Volume 6, Number 3, Pages 105–111 (Mi al1112)  

This article is cited in 1 scientific paper (total in 1 paper)

Some more examples of undecidable theories

M. A. Taislin


Abstract: 1. Let $L(\sigma)$ be a class of all relational systems of finite type $\sigma$. Suppose $\sigma'$ be a type which includes the type $\sigma$ and $D_{\sigma'}\ne D_{\sigma}$. Let $\sigma'(\Lambda )=1$ whenever $\Lambda \in D_{\sigma'}\setminus D_{\sigma}$. Let $K\subset L(\sigma)$ and $K(\sigma')=\{M\in L(\sigma')| M\upharpoonright \sigma\in K\}$. It is for a number of classes $K\subset L(\sigma)$ that the elementary theory of class $K(\sigma')$ is hereditarily undecidable. This holds for example, if class $K\subset L(\sigma)$ satisfies the conditions 1.-3.
2. When denoting $A(n,\tau,\Lambda )$ resp. $A^*(n,\tau,\Lambda )$ free algebras with $n$ free generators in the class of associative commutative $\tau$-nilpotent algebras over field $\Lambda $ resp. in the class of associative $\tau$-nilpotent algebras over field $\Lambda $ and putting $A(n,\Lambda )=\{A(n,\tau,\Lambda )| \tau=1,2,…\}$, $A^*(n,\Lambda )=\{A^*(n,\tau,\Lambda )| \tau=1,2,…\}$ it is proved that the elementary theories of the classes $A(n,\Lambda )$, $A^*(n,\Lambda )$ are hereditarily undecidable for $n\geqslant2$ if $\Lambda $ is field of characteristic $0$ and for $n\geqslant 3$ in each other cases. In all cases the elementary theory of class $A^*(2,\Lambda )$ is hereditarily undecidable.

Full text: PDF file (249 kB)

Bibliographic databases:
Received: 17.04.1967

Citation: M. A. Taislin, “Some more examples of undecidable theories”, Algebra i Logika. Sem., 6:3 (1967), 105–111

Citation in format AMSBIB
\Bibitem{Tai67}
\by M.~A.~Taislin
\paper Some more examples of undecidable theories
\jour Algebra i Logika. Sem.
\yr 1967
\vol 6
\issue 3
\pages 105--111
\mathnet{http://mi.mathnet.ru/al1112}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0224470}


Linking options:
  • http://mi.mathnet.ru/eng/al1112
  • http://mi.mathnet.ru/eng/al/v6/i3/p105

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. I. Kokorin, A. G. Pinus, “Decidability problems of extended theories”, Russian Math. Surveys, 33:2 (1978), 53–96  mathnet  crossref  mathscinet  zmath
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:11
    Full text:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021