Recursively categorical linear orderings
Author:
J. B. Remmel
Journal:
Proc. Amer. Math. Soc. 83 (1981), 387391
MSC:
Primary 03C57; Secondary 03C65, 03D45, 06A05
MathSciNet review:
624937
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Abstract: A recursive structure is recursively categorical if every recursive structure isomorphic to is recursively isomorphic to . We classify the recursively categorical linear orderings as precisely those recursive linear orderings which have only finitely many elements with an immediate successor.
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A. T. Nurtazin, Strong and weak constructivizations and computable families, Algebra and Logic 13 (1975), 177184.
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J. B. Remmel, Recursive isomorphisms of recursive Boolean algebras, J. Symbolic Logic (to appear).
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, Recursive Boolean algebras with recursive sets of atoms, J. Symbolic Logic (to appear).
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, Recursive isomorphisms of recursive Boolean algebras and atomic elements (in preparation).
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 S. S. Goncharov, Some properties of the constructivization of Boolean algebras, Sibirsk Mat. Ž. 16 (1975), 264278. MR 0381957 (52:2846)
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 A. I. Mal'cev, On recursive abelian groups, Soviet Math. 3 (1962), 14311432. 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), A552.
 [6]
 A. T. Nurtazin, Strong and weak constructivizations and computable families, Algebra and Logic 13 (1975), 177184.
 [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 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/S00029939198106249371
PII:
S 00029939(1981)06249371
Article copyright:
© Copyright 1981 American Mathematical Society
