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
- 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
- S. S. Gončarov, Certain properties of the constructivization of Boolean algebras, Sibirsk. Mat. Ž. 16 (1975), 264–278, 420. (loose errata) (Russian). MR 0381957
- A. I. Mal′cev, On recursive Abelian groups, Dokl. Akad. Nauk SSSR 146 (1962), 1009–1012 (Russian). MR 0151378 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).
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