论文标题
潜在主义体系的两次仿制
Bisimulations of potentialist systems
论文作者
论文摘要
潜在主义系统是基于嵌入的一阶Kripke模型。我定义了这些系统的分分概念，并提供了许多示例。给定一阶理论$ t $，系统$ \ mathrm {mod}（t）$由$ t $的所有型号组成。然后，我们可以在这些模型之间采用所有嵌入或所有子结构包含物。我表明，定义$ \ mathrm {mod}（t）$的这两种方法是比西二的。接下来，我将双仿真的概念与Ehrenfeucht-Fraïsé游戏的概括相关联，并用它来表明与无限语言相对于基本等效的双象相等的等效性。最后，我考虑了一个问题，即潜在主义系统何时与包含固定模型的系统具有比索性，提供过多的条件。
A potentialist system is a first-order Kripke model based on embeddings. I define the notion of bisimulation for these systems, and provide a number of examples. Given a first-order theory $T$, the system $\mathrm{Mod}(T)$ consists of all models of $T$. We can then take either all embeddings, or all substructure inclusions, between these models. I show that these two ways of defining $\mathrm{Mod}(T)$ are bitotally bisimilar. Next, I relate the notion of bisimulation to a generalisation of the Ehrenfeucht-Fraïsé game, and use this to show the equivalence of the existence of a bisimulation with elementary equivalence with respect to an infinitary language. Finally, I consider the question of when a potentialist system is bitotally bisimilar to a system containing set-many models, providing too different sufficient conditions.
