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The undecidability of theories of groupoids with an extra predicate


Authors: Solomon Garfunkel and James H. Schmerl
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
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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 [Enhancements On Off] (What's this?)

  • [1] Grace E. Bates, Free loops and nets and their generalizations, Amer. J. Math. 69 (1947), 499–550. MR 0021001, https://doi.org/10.2307/2371882
  • [2] 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
  • [3] S. Garfunkel, On the undecidability of certain finite theories. Trans. Amer. Math. Soc. (to appear).
  • [4] -, On the undecidability of certain classes of abelian groups with an extra unary predicate, Notices Amer. Math. Soc. 15 (1968), 632. Abstract #68T-439.
  • [5] S. Isard, Theories of algebraic structures with a distinguished subset, Notices Amer. Math. Soc. 14 (1967), 378. Abstract #644-67.
  • [6] 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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DOI: https://doi.org/10.1090/S0002-9939-1974-0325378-3
Article copyright: © Copyright 1974 American Mathematical Society