标题： 雷因哈特基数与最终支配函数 显示英文标题

标题： Reinhardt Cardinals and Eventually Dominating Functions

摘要： 我们证明了一个关于集合论宇宙自嵌入（Reinhardt嵌入）的初等等价和在序数上“最终支配”这些嵌入的函数的结果。 我们应用该结果来展示满足某些严格条件的初等等价的存在性，并且这些条件也让人联想到在更局部设置下的延展性。 在此基础上进一步发展这些概念，我们明确了加布里埃尔·戈德伯格在他的论文《可测基数和无选择公理》中证明的在Reinhardt嵌入下存在的一些大基数的本质。 最后，这些思想被用来提供Kunen不一致性的另一种证明。 显示英文摘要

摘要： We prove a result concerning elementary embeddings of the set-theoretic universe into itself (Reinhardt embeddings) and functions on ordinals that "eventually dominate" such embeddings. We apply that result to show the existence of elementary embeddings satisfying some strict conditions and that are also reminiscent of extendibility in a more local setting. Building further on these concepts, we make precise the nature of some large cardinals whose existence under Reinhardt embeddings was proven by Gabriel Goldberg in his paper "Measurable Cardinals and Choiceless Axioms." Finally, these ideas are used to present another proof of the Kunen inconsistency.