集合论模型的初始自嵌入
Initial self-embeddings of models of set theory
AI总结：
本文研究集合论模型的初始自嵌入，基于Friedman定理，探讨更大的适当初始嵌入族，其中像是传递子模型。
摘要：
根据Harvey Friedman（1973）的一个经典定理，ZF的每个可数非标准模型$\mathcal{M}$（具有足够强的片段）都有一个适当的秩初始自嵌入$j$，即$j$是$\mathcal{M}$的自嵌入，使得$j[\mathcal{M}]\subsetneq\mathcal{M}$，并且$j[\mathcal{M}]$中每个成员的序数秩小于$\mathcal{M}\setminus j[\mathcal{M}]$中每个元素的序数秩。这里我们研究集合论片段模型$\mathcal{M}$的更大的适当初始嵌入族$j$，其中$j$的像是$\mathcal{M}$的一个传递子模型。
英文摘要：
By a classical theorem of Harvey Friedman (1973), every countable nonstandard model $\mathcal{M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding $j$, i.e., $j$ is a self-embedding of $\mathcal{M}$ such that $j[\mathcal{M}]\subsetneq\mathcal{M}$, and the ordinal rank of each member of $j[\mathcal{M}]$ is less than the ordinal rank of each element of $\mathcal{M}\setminus j[\mathcal{M}]$. Here we investigate the larger family of proper initial-embeddings $j$ of models $\mathcal{M}$ of fragments of set theory, where the image of $j$ is a transitive submodel of $\mathcal{M}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
