论文标题
迭代的俱乐部射击和固定逻辑可构造模型
Iterated club shooting and the stationary-logic constructible model
论文作者
论文摘要
我们研究了$ c（\ mathtt {aa}）$的构建，即使用所谓的“ stastary-logic”构建的$ l $的内内模型。我们表明，有可能强迫$ l $的通用扩展，以获取$ v = c（\ mathtt {aa}）$的模型，并获得迭代$ c（\ mathtt {aa}）$ s的顺序的模型正在减少任意大订单类型的型号。为此，我们证明了使用相互固定组的俱乐部射击强迫迭代迭代的分配性和固定固定的保存特性，并引入了相互脂肪集的概念，即使无需迭代也可以产生更好的分布性结果。
We investigate iterating the construction of $C(\mathtt{aa})$, the $L$-like inner model constructed using the so-called "stationary-logic". We show that it is possible to force over generic extensions of $L$ to obtain a model of $V=C(\mathtt{aa})$, and to obtain models in which the sequence of iterated $C(\mathtt{aa})$s is decreasing of arbitrarily large order types. For this we prove distributivity and stationary-set preservation properties for countable iterations of club-shooting forcings using mutually stationary sets, and introduce the notion of mutually fat sets which yields better distributivity results even for uncountable iterations.
