Constructive Ultraproducts and Isomorphisms of Recursively Saturated Ultrapowers
Constructive Ultraproducts and Isomorphisms of Recursively Saturated Ultrapowers
复制标题
递归饱和超幂的构造性超积和同构
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
G. C. Nelson
中科院分区：
文献类型：
--
作者：
G. C. Nelson
一阶理论T的各种模型是由该理论的给定模型通过超积构造的推广而得到的。它表明，对于一个模型完整的理论，这种建设可以进行使用作为功能的超产品正是这些功能定义的条款在原来的语言的扩展。通过这种方式，人们得到了T的可数非标准模型，这些模型可以被赋予其他期望的性质，例如递归饱和。这些构造只使用模型论和递归论的最基本思想。证明了两个可数初等等价模型具有同构的递归饱和超幂。
Various models of a first order theory T are obtained from given models of that theory by generalizations of the ultraproduct construction. It is demonstrated that for a model complete theory this construction can be carried out using as functions for the ultraproduct exactly those functions defined by terms in an extension of the original language. In this way one obtains countable nonstandard models of T which can be endowed with other desirable properties such as being recursively saturated. These constructions use only the most basic ideas of model theory and recursion theory. Two countable elementarily equivalent models are shown to have recursive ultrapowers which are isomorphic and recursively saturated.