论文标题
普通贝尔空间中的laver树
Laver Trees in the Generalized Baire Space
论文作者
论文摘要
我们证明，对于无数的常规$κ$，对Laver强迫的任何合适的概括都必须增加Cohen $κ$ -REAL。我们还研究了与广义Laver强迫自然相关的二分法和理想。使用这种二分法，我们证明了以下更强的结果：如果$κ^{<κ} =κ$，那么每次$ <κ$ - $ - $ - 分布式树在$κ^κ$上都增加了$κ$κ$κ$ $ - 真实，这是在地面模型中连续函数的图像，在地面模型中，$κ$κ-$κ--亿美元。这是对广义Baire空间的研究的贡献，并回答了Arxiv的问题：1611.08140
We prove that any suitable generalization of Laver forcing to the space $ κ^κ$, for uncountable regular $κ$, necessarily adds a Cohen $κ$-real. We also study a dichotomy and an ideal naturally related to generalized Laver forcing. Using this dichotomy, we prove the following stronger result: if $ κ^{<κ}=κ$, then every $<κ$-distributive tree forcing on $κ^κ$ adding a dominating $κ$-real which is the image of the generic under a continuous function in the ground model, adds a Cohen $κ$-real. This is a contribution to the study of generalized Baire spaces and answers a question from arXiv:1611.08140
