Geodesic
Model-Completeness and Elementary Properties of Torsion Free Abelian Groups
Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 829-840

Voir la notice de l'article provenant de la source Cambridge University Press

The decidability of the elementary theory of abelian groups, and their complete classification by elementary properties (i.e. those formalizable in the lower predicate calculus (LPC) of formal logic), were established by W. Szmielew [13]. More general results were proved by Eklof and Fischer [2], and G. Sabbagh [12]. The rather formidable "high-power" techniques used in obtaining these remarkable results, and the length of the proofs (W. Szmielew's proof takes about 70 pages) triggered off several attempts at simplification. M. I. Kargapolov's proof [3] unfortunately turned out to be erroneous (cf. J. Mennicke's review in the Journal of Symbolic Logic, vol. 32, p. 535). 
Zakon, Elias. Model-Completeness and Elementary Properties of Torsion Free Abelian Groups. Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 829-840. doi: 10.4153/CJM-1974-078-4
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