标题： 算子鼠的精细结构 显示英文标题

标题： The fine structure of operator mice

摘要： 我们发展了算子先端（operator-premouse）的精细结构理论。 这些结构是对标准先端的一般化推广，在其中用抽象算子 $F$ 构造先端内部层次中的后继步骤，而不是使用詹森的 $J$-算子（后者计算原始闭包）。此类概念已在核心模型诱导论证中有过应用，但其理论尚未被详细发展。 我们定义了算子 $F$ 的精细凝聚性，并证明精细凝聚性和可迭代性一起确保了 $F$-先端具有基本的精细结构属性，包括标准参数的普适性和坚固性。 显示英文摘要

摘要： We develop the fine structure theory of operator-premice. These are a generalization of standard premice, in which an abstract operator $F$ is used to form the successor steps in the internal hierarchy of the premouse, instead of Jensen's $J$-operator (which computes rudimentary closure). Such notions have seen applications in core model induction arguments, but their theory has not previously been developed in detail. We define fine condensation for operators $F$ and show that fine condensation and iterability together ensure that $F$-mice have the fundamental fine structural properties including universality and solidity of the standard parameter.