Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Recognizing the real line


Authors: Yuri Gurevich and W. Charles Holland
Journal: Trans. Amer. Math. Soc. 265 (1981), 527-534
MSC: Primary 03C60; Secondary 03C65, 06F15
DOI: https://doi.org/10.1090/S0002-9947-1981-0610963-X
MathSciNet review: 610963
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A certain elementary statement about the group of automorphisms of the real line $ \mathbf{R}$ is sufficient to characterize $ \mathbf{R}$ among homogeneous chains. A similar result holds for the chain of rational numbers.


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

  • [1] A. M. W. Glass, Ordered permutation groups, Bowling Green State University, 1976. MR 0422105 (54:10097)
  • [2] W. C. Holland, The lattice-ordered group of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399-403. MR 0158009 (28:1237)
  • [3] -, Transitive ordered permutation groups, Math. Z. 87 (1965), 420-433. MR 0178052 (31:2310)
  • [4] -, Trying to recognize the real line, Ordered Groups, Lecture Notes in Pure and Appl. Math., Dekker, New York, 1980. MR 601621 (82i:06022)
  • [5] M. Jambu-Giraudet, Théorie des modèles des groups d'automorphismes d'ensembles totalment ordonné, Thèse $ {3^{me}}$ cycle, Univ. Paris VII, 1979.
  • [6] S. H. McCleary, Groups of homeomorphisms with manageable automorphism groups, Comm. Algebra 6 (1978), 497-528. MR 484757 (81e:20045)
  • [7] R. McKenzie, On elementary types of symmetric groups, Algebra Universalis 1 (1971), 13-20. MR 0286643 (44:3852)
  • [8] A. G. Pinus, On elementary definability of symmetric groups, Algebra Universalis 3 (1973), 59-66. MR 0337594 (49:2363)
  • [9] S. Shelah, First order theory of permutation groups, Israel J. Math. 14 (1973), 149-162; 15 (1973), 437-441. MR 0416909 (54:4972)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03C60, 03C65, 06F15

Retrieve articles in all journals with MSC: 03C60, 03C65, 06F15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0610963-X
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society