QUANTIFIER ELIMINATION IN ORDERED ABELIAN GROUPS

Confluentes Mathematici

CLUCKERS, RAF¹  HALUPCZOK, IMMANUEL² 

[1] Katholieke Universiteit Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium;Université Lille 1, Laboratoire Painlevé, CNRS – UMR 8524, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex, France

关键词: Ordered abelian groups;    quantifier elimination;    cell decomposition;    piecewise linear;    model theory;    ordered sets;    Presburger language;   

DOI  :  10.1142/S1793744211000473

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in the group is a union of a family of quantifier free definable sets, where the parameter of the family runs over a set definable (with quantifiers) in a sort which carries the structure of an ordered set with some additional unary predicates. As a corollary, we find that all definable functions in ordered abelian groups are piecewise linear on finitely many definable pieces.

【 授权许可】

Unknown