有限可换主理想环上广义模理论T(Q)的模型可归约性

Model Reducibility of Generalized FCPIR Modules Theory T(Q)

本文在对两个模型定义了α，β，ｎ－扩充的基础上，利用广义ＥｈｒｅｎｆｅｕｃｈｔＧａｍｅ理论证明了Ｔ（Ｑ）的模型可归约性，从而得到：对无限基数α，β，（α≥β＞０），对于模型ＡαＴＲ（Ｑ）则存在模型ＢβＴＲ（Ｑ）使得Ａα≡βＢ；以及任意自然数ｍ＞０，存在模型Ｃ０ＴＲ（Ｑ），使得Ａα≡ｍ０Ｃ．

We deal with the model reducibility of the generalized theory T(Q) of modules on FCPIR, finitely communtative principle ideal ring. By Ehrenfeucht Games Method we confirmed that the model of T(Q) is reducible. That is, for infinite cardinalities α,β with αβ< 0 , and a α model A, there exists a β model B s.t.  A α≡ βB; and further, for a nature number m>0, there exists a  0 model C, s.t. A α≡m  0 C.