论文标题
Magidor迭代和超能力对地面模型的限制
The Magidor Iteration and Restrictions of Ultrapowers to the Ground Model
论文作者
论文摘要
我们研究了Prikry强迫的Magidor迭代，低于可测量的$κ$。我们首先表征了所有正常测量$κ$都在通用扩展中携带，并在\ cite {ben2014forcing}的主要结果上构建并扩展了。然后，对于每种常规措施，我们都证明其超能源的限制（从通用扩展到地面模型）是正常措施的迭代超级迭代的超级效力。这是没有核心模型理论假设的； $ \ mbox {gch} _ {\ leqκ} $在地面模型中就足够了。
We study the Magidor iteration of Prikry forcings below a measurable limit of measurables $ κ$. We first characterize all the normal measures $ κ$ carries in the generic extension, building on and extending the main result of \cite{ben2014forcing}. Then, for every such normal measure, we prove that the restriction of its ultrapower, from the generic extension to the ground model, is an iterated ultrapower of $ V $ by normal measures. This is done without core model theoretic assumptions; $ \mbox{GCH}_{\leq κ} $ in the ground model suffices.
