Quantifier elimination in ordered abelian groups
Confluentes Mathematici, Tome 3 (2011) no. 4, pp. 587-615.
Publié le :
DOI : 10.1142/S1793744211000473
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Cluckers, Raf; Halupczok, Immanuel. Quantifier elimination in ordered abelian groups. Confluentes Mathematici, Tome 3 (2011) no. 4, pp. 587-615. doi : 10.1142/S1793744211000473. http://www.numdam.org/articles/10.1142/S1793744211000473/

[1] O. Belegradek, V. Verbovskiy and F. O. Wagner, Coset-minimal groups, Ann. Pure Appl. Logic 121 (2003) 113–143.

[2] R. Cluckers and I. Halupczok, Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry, 2010, to appear in Selecta Mathematica.

[3] Y. Gurevich, Elementary properties of ordered Abelian groups, Am. Math. Soc., Transl., II. Ser. 46 (1964) 165–192 (English, Russian original).

[4] , The decision problem for some algebraic theories, 1968, Doctor of Mathemat- ics dissertation.

[5] Y. Gurevich and P. H. Schmitt, The theory of ordered abelian groups does not have the independence property, Trans. Amer. Math. Soc. 284 (1984) 171–182.

[6] I. Halupczok, A language for quantifier elimination in ordered abelian groups, Séminaire de Structures Algébriques Ordonnées 2009–2010, eds. F. Delon, M. A. Dick- mann and D. Gondard, Équipe de Logique Mathématique, Vol. 85 (Université Paris 7, 2011).

[7] B. Poizat, Cours de théorie des modèles, Bruno Poizat, Lyon, 1985, Une introduc- tion à la logique mathématique contemporaine. [An introduction to contemporary mathematical logic].

[8] M. Rubin, Theories of linear order, Israel J. Math. 17 (1974) 392–443.

[9] P. H. Schmitt, Model theory of ordered abelian groups, 1982, Habilitationsschrift.

[10] , Model- and substructure-complete theories of ordered abelian groups, in Mod- els and Sets (Aachen, 1983), Lecture Notes in Math., Vol. 1103 (Springer, 1984), pp. 389–418.

[11] V. Weispfenning, Elimination of quantifiers for certain ordered and lattice-ordered abelian groups, Proc. of the Model Theory Meeting (Univ. Brussels, Brussels/Univ. Mons, Mons, 1980), Vol. 33 (1981) 131–155.

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