论文标题
离散集可以在有序的Abelian群体的强大扩展中定义
Discrete sets definable in strong expansions of ordered Abelian groups
论文作者
论文摘要
我们研究了无限离散集的结构D在有序的Abelian群体的扩展中可定义，其理论强大且完全完整，特别强调了由连续元素之间的差异组成的集合D'。特别是，如果结构的负担最多是n，则将操作D d d'n次施加到n次的结果必须是有限集（定理1.1）。在结构密集排序并具有负担2的情况下，我们表明在结构的某些基本扩展中，必须定义任何可定义的单个离散集（r; <， +，z）（定理1.3）。
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive elements. In particular, if the burden of the structure is at most n, then the result of applying the operation taking D to D' n times must be a finite set (Theorem 1.1). In the case when the structure is densely ordered and has burden 2, we show that any definable unary discrete set must be definable in some elementary extension of the structure (R; <, +, Z) (Theorem 1.3).
