Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-25T11:52:07.439Z Has data issue: false hasContentIssue false
  • English
  • Français

Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets

Published online by Cambridge University Press:  12 March 2014

James H. Schmerl
James H. Schmerl*
Affiliation:
University of Connecticut, Storrs, Connecticut 06268
Get access Rights & Permissions [Opens in a new window]

Abstract

Every ℵ0-categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ0-categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ0-categorical partially ordered set not embedding one of them has a decidable theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 1 , March 1981 , pp. 101 - 120
Copyright
Copyright © Association for Symbolic Logic 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Rosenstein, J. G., ℵ0-categoricity of linear orderings, Fundamenta Mathematieae, vol. 44 (1969), pp. 1–5.Google Scholar
[2]Rubin, M., Theories of linear order, Israel Journal of Mathematicae, vol. 17 (1974), pp. 392–443.CrossRefGoogle Scholar
[3]Schmerl, J. H., The decidability of some ℵ0-categorical theories, Colloquium Mathematicum, vol. 36 (1976), pp. 165–169.CrossRefGoogle Scholar
[4]Schmerl, J. H., On ℵ0-categoricity and the theory of trees, Fundamenta Mathematicae, vol. 94 (1977), pp. 121–128.CrossRefGoogle Scholar
[5]Schmerl, J. H., ℵ0-categoricity of partially ordered sets of width 2, Proceedings of the American Mathematical Society, vol. 63 (1977), pp. 299–305.Google Scholar
[6]Schmerl, J. H., Decidability and ℵ0-categoricity of theories of partially ordered sets, this Journal, vol. 45 (1980), pp. 585–611.Google Scholar
[7]Schmerl, J. H., ℵ0-categoricity and comparability graphs, Logic Colloquium '77, North-Holland, Amsterdam, 1978, pp. 221–228CrossRefGoogle Scholar