Recursively categorical linear orderings

Author:
J. B. Remmel

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[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****[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****[3]**A. I. Mal′cev,*On recursive Abelian groups*, Dokl. Akad. Nauk SSSR**146**(1962), 1009–1012 (Russian). MR**0151378****[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*-*groups*(Proc. Conf. Math. Logic, Univ. Connecticut), Lecture Notes in Math, (to appear).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
03C57,
03C65,
03D45,
06A05

Retrieve articles in all journals with MSC: 03C57, 03C65, 03D45, 06A05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0624937-1

Article copyright:
© Copyright 1981
American Mathematical Society