Some model theory of Abelian groups

Journal of Symbolic Logic 37 (2):335-342 (1972)
  Copy   BIBTEX

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

Categories

Keywords

Reprint years

DOI

10.2307/2272976

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,202

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Perfect MV-Algebras Are Categorically Equivalent to Abelian l-Groups.Antonio Di Nola & Ada Lettieri - 1994 - Studia Logica 53 (3):417-432.
Undecidable lt theories of topological Abelian groups.Gregory L. Cherlin & Peter H. Schmitt - 1981 - Journal of Symbolic Logic 46 (4):761 - 772.
A model-theoretic proof for P ≠ NP over all infinite Abelian groups.Mihai Prunescu - 2002 - Journal of Symbolic Logic 67 (1):235 - 238.
A common abstraction of MV-Algebras and Abelian l-groups.Francesco Paoli - 2000 - Studia Logica 65 (3):355-366.
Metamathematics of Ulm theory.Harvey Friedman - manuscript
Some model theory for almost real closed fields.Françoise Delon & Rafel Farré - 1996 - Journal of Symbolic Logic 61 (4):1121-1152.
On inverse γ-systems and the number of l∞λ- equivalent, non-isomorphic models for λ singular.Saharon Shelah & Pauli Väisänen - 2000 - Journal of Symbolic Logic 65 (1):272 - 284.
Actions of groups of finite Morley rank on small abelian groups.Adrien Deloro - 2009 - Bulletin of Symbolic Logic 15 (1):70-90.
The model theory of finitely generated finite-by-Abelian groups.Francis Oger - 1984 - Journal of Symbolic Logic 49 (4):1115-1124.

Analytics

Added to PP
2009-01-28

Downloads
254 (#76,006)

6 months
18 (#127,601)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Classes Closed Under Substructures and Direct Limits.Paul C. Eklof - 1977 - Mathematical Logic Quarterly 23 (27-30):427-430.

Add more citations

References found in this work

On Model-Completeness.Per Lindström - 1964 - Theoria 30 (3):183-196.
Model-completions and modules.P. Eklof - 1971 - Annals of Mathematical Logic 2 (3):251.
The elementary theory of abelian groups.Paul C. Eklof - 1972 - Annals of Mathematical Logic 4 (2):115.

Add more references