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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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Recursively categorical linear orderings
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by J. B. Remmel PDF
Proc. Amer. Math. Soc. 83 (1981), 387-391 Request permission

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
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  • A. B. Manaster and J. B. Remmel, Recursively categorical decidable dense two dimensional partial orderings (to appear). P. E. LaRoche, Recursively presented Boolean algebras, Notices Amer. Math. Soc. 24 (1977), A-552. A. T. Nurtazin, Strong and weak constructivizations and computable families, Algebra and Logic 13 (1975), 177-184. J. B. Remmel, Recursive isomorphisms of recursive Boolean algebras, J. Symbolic Logic (to appear). —, Recursive Boolean algebras with recursive sets of atoms, J. Symbolic Logic (to appear). —, Recursive isomorphisms of recursive Boolean algebras and atomic elements (in preparation). 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
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 387-391
  • MSC: Primary 03C57; Secondary 03C65, 03D45, 06A05
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0624937-1
  • MathSciNet review: 624937