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Some model theory of abelian groups

  • Paul C. Eklof (a1)

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.

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[1]Eklof, P. and Fisher, E., The elementary theory ofabelian groups, Annals of Mathematical Logic, vol. 4 (1972).
[2]Eklof, P. and Sabbagh, G., Model-completions and modules, Annals of Mathematical Logic, vol. 2 (1971), pp. 251295.
[3]Fuchs, L., Infinite abelian groups, Academic Press, New York, 1970.
[4]Lindström, P., On model-completeness, Theoria, vol. 30 (1964), pp. 183196.
[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. 909912.
[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. 12891292.
[7]Szmielew, W., Elementary properties of abelian groups, Fundamenta Mathematicae, vol. 41 (1955), pp. 203271.

Some model theory of abelian groups

  • Paul C. Eklof (a1)

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