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

 

Recursively categorical linear orderings


Author: J. B. Remmel
Journal: Proc. Amer. Math. Soc. 83 (1981), 387-391
MSC: Primary 03C57; Secondary 03C65, 03D45, 06A05
MathSciNet review: 624937
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Abstract: A recursive structure $ \mathcal{A}$ is recursively categorical if every recursive structure $ \mathcal{A}'$ isomorphic to $ \mathcal{A}$ is recursively isomorphic to $ \mathcal{A}$. We classify the recursively categorical linear orderings as precisely those recursive linear orderings $ L$ which have only finitely many elements with an immediate successor.


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

  • [1] C. J. Ash and A. Nerode, Intrinsically recursive relations, Aspects of effective algebra (Clayton, 1979) Upside Down A Book Co., Yarra Glen, Vic., 1981, pp. 26–41. MR 629248 (83a:03039)
  • [2] S. S. Gončarov, Certain properties of the constructivization of Boolean algebras, Sibirsk. Mat. Ž. 16 (1975), 264–278, 420. (loose errata) (Russian). MR 0381957 (52 #2846)
  • [3] A. I. Mal′cev, On recursive Abelian groups, Dokl. Akad. Nauk SSSR 146 (1962), 1009–1012 (Russian). MR 0151378 (27 #1363)
  • [4] A. B. Manaster and J. B. Remmel, Recursively categorical decidable dense two dimensional partial orderings (to appear).
  • [5] P. E. LaRoche, Recursively presented Boolean algebras, Notices Amer. Math. Soc. 24 (1977), A-552.
  • [6] A. T. Nurtazin, Strong and weak constructivizations and computable families, Algebra and Logic 13 (1975), 177-184.
  • [7] J. B. Remmel, Recursive isomorphisms of recursive Boolean algebras, J. Symbolic Logic (to appear).
  • [8] -, Recursive Boolean algebras with recursive sets of atoms, J. Symbolic Logic (to appear).
  • [9] -, Recursive isomorphisms of recursive Boolean algebras and atomic elements (in preparation).
  • [10] R. L. Smith, Two theorems on autostability in $ p$-groups (Proc. Conf. Math. Logic, Univ. Connecticut), Lecture Notes in Math, (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0624937-1
PII: S 0002-9939(1981)0624937-1
Article copyright: © Copyright 1981 American Mathematical Society