Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T19:48:53.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Some model theory of abelian groups

Published online by Cambridge University Press:  12 March 2014

Paul C. Eklof
Paul C. Eklof*
Affiliation:
Stanford University, Stanford, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the relations between abelian groups B and C that every universal (resp. universal-existential) sentence true in B is also true in C, and give algebraic criteria for these relations to hold. As a consequence we characterize the inductive complete theories of abelian groups and prove that they are exactly the model-complete theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 37 , Issue 2 , June 1972 , pp. 335 - 342
Copyright
Copyright © Association for Symbolic Logic 1972

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]Eklof, P. and Fisher, E., The elementary theory ofabelian groups, Annals of Mathematical Logic, vol. 4 (1972).CrossRefGoogle Scholar
[2]Eklof, P. and Sabbagh, G., Model-completions and modules, Annals of Mathematical Logic, vol. 2 (1971), pp. 251–295.CrossRefGoogle Scholar
[3]Fuchs, L., Infinite abelian groups, Academic Press, New York, 1970.Google Scholar
[4]Lindström, P., On model-completeness, Theoria, vol. 30 (1964), pp. 183–196.Google Scholar
[5]Sabbagh, G., Aspects logiques de la pureté dans les modules, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Séries A, vol. 271 (1970), pp. 909–912.Google Scholar
[6]Sabbagh, G., Sous-modules purs, existentiellement clos et elementaires, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Séries A, vol. 272 (1971), pp. 1289–1292.Google Scholar
[7]Szmielew, W., Elementary properties of abelian groups, Fundamenta Mathematicae, vol. 41 (1955), pp. 203–271.CrossRefGoogle Scholar