论文标题
算术模型的自我安装；固定点，小型模型和可扩展性
Self-embeddings of models of arithmetic; fixed points, small submodels, and extendability
论文作者
论文摘要
In this paper we will show that for every cut $ I $ of any countable nonstandard model $ \mathcal{M} $ of $ \mathrm{I}Σ_{1} $, each $ I $-small $ Σ_{1} $-elementary submodel of $ \mathcal{M}$ is of the form of the set of fixed points of some proper initial self-embedding of $ \ Mathcal {M} $ IFF $ i $是$ \ Mathcal {M} $的强切。尤其是，此功能将为我们提供一些等效条件，并在给定的可计数模型$ \ Mathcal {m} $ $ \ Mathrm {i}σ_{1} $中削减标准剪切的强度。此外，我们还将找到一些标准，以扩展$ \ mathrm {i}σ_{1} $的可计数非标准模型的初始自我安装。
In this paper we will show that for every cut $ I $ of any countable nonstandard model $ \mathcal{M} $ of $ \mathrm{I}Σ_{1} $, each $ I $-small $ Σ_{1} $-elementary submodel of $ \mathcal{M}$ is of the form of the set of fixed points of some proper initial self-embedding of $ \mathcal{M} $ iff $ I $ is a strong cut of $ \mathcal{M} $. Especially, this feature will provide us with some equivalent conditions with the strongness of the standard cut in a given countable model $ \mathcal{M} $ of $ \mathrm{I}Σ_{1} $. In addition, we will find some criteria for extendability of initial self-embeddings of countable nonstandard models of $ \mathrm{I}Σ_{1} $ to larger models.
