标题： 对算术模型复杂性的分类 显示英文标题

标题： Classifying the complexity of models of arithmetic

摘要： 我们对皮亚诺算术模型的可能Scott复杂度进行分类。 我们通过首先对彩色线性序进行完整的Scott分析，并从这些彩色序中构造皮亚诺算术模型，从而构造出特定复杂度的模型。 我们还提供了某些Scott复杂度与皮亚诺算术经典模型理论中的概念之间的紧密联系，例如素数、有限生成和递归饱和。 这一努力提供了一套强大的工具来理解皮亚诺算术模型。 显示英文摘要

摘要： We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored linear orderings and constructing models of Peano arithmetic from these colored orderings. We also provide tight connections of certain Scott complexities with notions from the classical theory of models of Peano arithmetic, such as prime, finitely generated, and recursively saturated. This effort provides a powerful set of tools to understand the models of Peano arithmetic.