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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Degrees of unsolvability
of first order decision problems
for finitely presented groups


Author: Oleg V. Belegradek
Journal: Proc. Amer. Math. Soc. 124 (1996), 623-625
MSC (1991): Primary 03D40, 03D30, 20F10, 20F18
MathSciNet review: 1307493
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Abstract: We show that for any arithmetical $m$-degree $\mathbf{d}$ there is a first order decision problem $\mathbf{P}$ such that $\mathbf{P}$ has $m$-degree $\mathbf{d}$ for the free 2-step nilpotent group of rank 2. This implies a conjecture of Sacerdote.


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Additional Information

Oleg V. Belegradek
Affiliation: Kemerovo State University, Kemerovo 650043, Russia
Email: beleg@kaskad.kemerovo.su

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03209-1
PII: S 0002-9939(96)03209-1
Keywords: First order decision problem, $m$-degree
Received by editor(s): August 19, 1994
Additional Notes: The author was partially supported by the AMS fSU Aid Fund.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society