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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The undecidability of theories of groupoids with an extra predicate
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by Solomon Garfunkel and James H. Schmerl PDF
Proc. Amer. Math. Soc. 42 (1974), 286-289 Request permission

Abstract:

Let T be any theory in the language of groupoids, and let $T’$ be the same theory considered now in the language with an extra unary predicate. If some model of T has a substructure which is an infinite cancellative groupoid, then $T’$ is hereditarily undecidable.
References
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  • Ju. L. Eršov, I. A. Lavrov, A. D. Taĭmanov, and M. A. Taĭclin, Elementary theories, Uspehi Mat. Nauk 20 (1965), no. 4 (124), 37–108 (Russian). MR 0186553
  • S. Garfunkel, On the undecidability of certain finite theories. Trans. Amer. Math. Soc. (to appear). —, On the undecidability of certain classes of abelian groups with an extra unary predicate, Notices Amer. Math. Soc. 15 (1968), 632. Abstract #68T-439. S. Isard, Theories of algebraic structures with a distinguished subset, Notices Amer. Math. Soc. 14 (1967), 378. Abstract #644-67.
  • Michael O. Rabin, A simple method for undecidability proofs and some applications, Logic, Methodology and Philos. Sci. (Proc. 1964 Internat. Congr.), North-Holland, Amsterdam, 1965, pp. 58–68. MR 0221924
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 286-289
  • MSC: Primary 02G05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0325378-3
  • MathSciNet review: 0325378