THE THEORY OF ORDERED ABELIAN GROUPS DOES NOT HAVE THE INDEPENDENCE PROPERTY
THE THEORY OF ORDERED ABELIAN GROUPS DOES NOT HAVE THE INDEPENDENCE PROPERTY
复制标题
有序阿贝尔群理论不具有独立性
DOI：
10.1090/s0002-9947-1984-0742419-0
复制
发表时间：
1984
影响因子：
1.3
通讯作者：
P. Schmitt
中科院分区：
文献类型：
--
作者：
Y. Gurevich;P. Schmitt
摘要。证明了所有有序阿贝尔群的完备理论都不具有独立性，从而回答了B. Poizat的一个问题。主要工具是Yuri Gurevich博士论文和p.h. Schmitt的《有序阿贝尔群的初等性质》中的一个结果，它将有序阿贝尔群上的命题转化为色链上的命题。我们还证明了色链理论中的每一个ra型最多有2 '同子，从而加强了B. Poizat的一个结果。背景和介绍。独立性是S. Shelah在bbb . definition中引入的性质之一。一个完备的理论T被称为具有独立性，如果有一个公式0:T\j(3xs\ f\ v(xs,cl)k A -。<p(f,c'): s c fc是一致的。为了传达这个定义的相关性，我们记住（逻辑）稳定性理论的两个结果。
ABSTRACT. We prove that no complete theory of ordered abelian groups hasthe independence property, thus answering a question by B. Poizat. The maintool is a result contained in the doctoral dissertation of Yuri Gurevich and alsoin P. H. Schmitt's Elementary properties of ordered abelian groups, which basicallytransforms statements on ordered abelian groups into statements on colouredchains. We also prove that every ra-type in the theory of coloured chains hasat most 2" coheirs, thereby strengthening a result by B. Poizat. 0. Background and introduction. The independence property is one of theproperties introduced by S. Shelah in [16].DEFINITION. A complete theory T is said to have the independence property, if there is a formula 0: T\j(3xs\ f\ v(xs,cl)k A -.<p(f,c') : s C fc is consistent. To convey an idea of the relevance of this definition we remember two resultsfrom (logical) stability theory.