有序阿贝尔群中的量词消去

Q4 Mathematics

Confluentes Mathematici Pub Date : 2011-10-14 DOI:10.1142/S1793744211000473

R. Cluckers, Immanuel Halupczok

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引用次数: 34

摘要

在合适的语言条件下，给出了全序阿贝尔群理论中量词消去的一个新的证明。更准确地说，这只是以下意义上的“相对于有序集合的量词消去”。群中的每个可定义集合都是一组没有量词的可定义集合的并集，其中该族的参数遍历一个可定义集合(带有量词)，其排序带有带有一些附加一元谓词的有序集合的结构。作为一个推论，我们发现有序阿贝尔群中的所有可定义函数在有限多个可定义块上都是分段线性的。

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Quantifier elimination in ordered abelian groups

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.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.