标题： HOD对可接受结构的分析 显示英文标题

标题： Analysis of HOD for Admissible Structures

摘要： 设 $n \geq 1$ 并假设存在一个伍丁基数。 对于$x \in \mathbb{R}$让$\alpha_x$成为最小的$\beta$使得 \[ L_\beta [x] \models \Sigma_n \text{-KP} + \exists \kappa (``\kappa \text{ is inaccessible and }\kappa^+ \text{ exists}"). \] 我们适应$\text{HOD}^{L[x,G]}$的分析作为一种策略鼠标到 $L_{\alpha_x}[x,G]$对于一个实数的锥体$x$。 也就是说，我们识别一个鼠标$\mathcal{M}^{\text{n-ad}}$并定义一个类$H \subseteq L_{\alpha_x}[x,G]$作为$\text{HOD}^{L[x,G]} \subseteq L[x,G]$的自然模拟，并证明$H = M_\infty[\Sigma_0]$，其中$M_\infty$是$\mathcal{M}^{\text{n-ad}}$的迭代，$\Sigma_0$是其迭代策略的一部分。 显示英文摘要

摘要： Let $n \geq 1$ and assume that there is a Woodin cardinal. For $x \in \mathbb{R}$ let $\alpha_x$ be the least $\beta$ such that \[ L_\beta [x] \models \Sigma_n \text{-KP} + \exists \kappa (``\kappa \text{ is inaccessible and }\kappa^+ \text{ exists}"). \] We adapt the analysis of $\text{HOD}^{L[x,G]}$ as a strategy mouse to $L_{\alpha_x}[x,G]$ for a cone of reals $x$. That is, we identify a mouse $\mathcal{M}^{\text{n-ad}}$ and define a class $H \subseteq L_{\alpha_x}[x,G]$ as a natural analogue of $\text{HOD}^{L[x,G]} \subseteq L[x,G]$, and show that $H = M_\infty[\Sigma_0]$, where $M_\infty$ is an iterate of $\mathcal{M}^{\text{n-ad}}$ and $\Sigma_0$ a fragment of its iteration strategy.