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Undecidability of the theory of abelian groups with a subgroup

Author: Walter Baur
Journal: Proc. Amer. Math. Soc. 55 (1976), 125-128
MSC: Primary 02G05
MathSciNet review: 0416890
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Abstract: The theory of abelian groups with an additional predicate denoting a subgroup is undecidable.

References [Enhancements On Off] (What's this?)

  • [1] Walter Baur, ℵ₀-categorical modules, J. Symbolic Logic 40 (1975), 213–220. MR 0369047
  • [2] Martin Davis, Computability and unsolvability, McGraw-Hill Series in Information Processing and Computers, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR 0124208
  • [3] Paul Eklof and Gabriel Sabbagh, Model-completions and modules, Ann. Math. Logic 2 (1970/1971), no. 3, 251–295. MR 0277372
  • [4] G. T. Kozlov and A. I. Kokorin, An elementary theory of torsion-free abelian groups with a predicate that distinguishes a subgroup, Algebra i Logika 8 (1969), 320–334 (Russian). MR 0258617
  • [5] Saharon Shelah, Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory, Ann. Math. Logic 3 (1971), no. 3, 271–362. MR 0317926
  • [6] W. Szmielew, Elementary properties of Abelian groups, Fund. Math. 41 (1955), 203–271. MR 0072131

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Article copyright: © Copyright 1976 American Mathematical Society