论文标题
甚至列音和昆宁的不一致
Even ordinals and the Kunen inconsistency
论文作者
论文摘要
本文在不假定选择公理的情况下，有助于超出库宁矛盾或无数宽大的基本公理的理论。本文的第一部分研究了一个周期性现象：假设无数较大的基本公理，累积层次结构的特性变成了偶数和奇数等级之间的交替。本文的第二部分探讨了无选的大型基本公理下的超滤器的结构，从而利用了这些公理意味着作者超级公理的弱形式的事实。本文的第三部分也是最后一部分研究了无选的大型红衣主教的一致性强度，包括假设DC，存在从$ v_ {λ+3} $到$ v_ {λ+3} $的基本嵌入的证明，意味着ZFC+$ i_0 $的一致性。根据Schlutzenberg的最新结果，一个基本嵌入$ v_ {λ+2} $到$ v_ {λ+2} $不足。
This paper contributes to the theory of large cardinals beyond the Kunen inconsistency, or choiceless large cardinal axioms, in the context where the Axiom of Choice is not assumed. The first part of the paper investigates a periodicity phenomenon: assuming choiceless large cardinal axioms, the properties of the cumulative hierarchy turn out to alternate between even and odd ranks. The second part of the paper explores the structure of ultrafilters under choiceless large cardinal axioms, exploiting the fact that these axioms imply a weak form of the author's Ultrapower Axiom. The third and final part of the paper examines the consistency strength of choiceless large cardinals, including a proof that assuming DC, the existence of an elementary embedding from $V_{λ+3}$ to $V_{λ+3}$ implies the consistency of ZFC + $I_0$. By a recent result of Schlutzenberg, an elementary embedding from $V_{λ+2}$ to $V_{λ+2}$ does not suffice.
