Recognizing the real line

Gurevich, Yuri; Holland, W. Charles

doi:10.1090/S0002-9947-1981-0610963-X

Recognizing the real line
HTML articles powered by AMS MathViewer

by Yuri Gurevich and W. Charles Holland

Trans. Amer. Math. Soc. 265 (1981), 527-534

DOI: https://doi.org/10.1090/S0002-9947-1981-0610963-X

PDF | Request permission

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

A. M. W. Glass, Ordered permutation groups, Bowling Green State University, Bowling Green, Ohio, 1976. MR 0422105
Charles Holland, The lattice-ordered groups of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399–408. MR 158009
Charles Holland, Transitive lattice-ordered permutation groups, Math. Z. 87 (1965), 420–433. MR 178052, DOI 10.1007/BF01111722
W. Charles Holland, Trying to recognize the real line, Ordered groups (Proc. Conf., Boise State Univ., Boise, Idaho, 1978), Lecture Notes in Pure and Appl. Math., vol. 62, Dekker, New York, 1980, pp. 131–134. MR 601621

Théorie des modèles des groups d’automorphismes d’ensembles totalment ordonné

Stephen H. McCleary, Groups of homeomorphisms with manageable automorphism groups, Comm. Algebra 6 (1978), no. 5, 497–528. MR 484757, DOI 10.1080/00927877808822256
Ralph McKenzie, On elementary types of symmetric groups, Algebra Universalis 1 (1971), no. 1, 13–20. MR 286643, DOI 10.1007/BF02944950
A. G. Pinus, Elementary definability of symmetry groups, Algebra Universalis 3 (1973), 59–66. MR 337594, DOI 10.1007/BF02945104
Saharon Shelah, First order theory of permutation groups, Israel J. Math. 14 (1973), 149–162; errata, ibid. 15 (1973), 437–441. MR 416909, DOI 10.1007/BF02762670