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 | References | Similar Articles | Additional Information

Abstract: We show that for any arithmetical -degree there is a first order decision problem such that has -degree for the free 2-step nilpotent group of rank 2. This implies a conjecture of Sacerdote.

**B**O. V. Belegradek,*The Mal′cev correspondence revisited*, Proceedings of the International Conference on Algebra, Part 1 (Novosibirsk, 1989) Contemp. Math., vol. 131, Amer. Math. Soc., Providence, RI, 1992, pp. 37–59. MR**1175761****M**A. I. Maltsev,*A correspondence between rings and groups*, Mat. Sb. (N.S.)**50**(1960), 257--

266; English transl.,*The metamathematics of algebraic systems. Collected papers: 1936--1967, North-Holland, 1971, pp. 124--137*.**S1**George S. Sacerdote,*Some undecidable problems in group theory*, Proc. Amer. Math. Soc.**36**(1972), 231–238. MR**0320119**, 10.1090/S0002-9939-1972-0320119-6**S2**George S. Sacerdote,*On a problem of Boone*, Math. Scand.**31**(1972), 111–117. MR**0318324**

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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

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