论文标题
强迫两种类型的模型的对称系统
Forcing with Symmetric Systems of Models of Two Types
论文作者
论文摘要
本注释的主要目的是提出Neeman强迫的矩阵版本，其中两种模型序列。从某种意义上说，此处定义的强迫可以看作是Asperó-Mota纯侧条件强迫从Arxiv：1203.1235和Arxiv：1206.6724的概括。在我们的情况下，强迫将由某些$ h（κ）$的可数和不可数基本码的对称系统组成，从尼曼的意义上讲，这将由相关的交叉点关闭。本说明的目的是表明，这种强迫通过证明$ h（κ）$的可计数subsodels和对数的封闭子模型的$ h（κ）$ h（κ）尺寸$ \ alleph_1 $非常适合所有红衣主教，并且具有$ \ alleph_3 $ -cc。此外，我们将证明它保留了$ 2^{\ aleph_1} = \ aleph_2 $。
The main purpose of this note is to present a matrix version of Neeman's forcing with sequences of models of two types. In some sense, the forcing defined here can be seen as a generalization of Asperó-Mota's pure side condition forcing from arXiv:1203.1235 and arXiv:1206.6724. In our case, the forcing will consist of certain symmetric systems of countable and uncountable elementary submodels of some $H(κ)$, which will be closed by the relevant intersections, in Neeman's sense. The goal of this note is to show that this forcing preserves all cardinals by showing that it is strongly proper for the class of countable submodels of $H(κ)$ and for the class of countably closed submodels of $H(κ)$ of size $\aleph_1$, and that it has has the $\aleph_3$-cc. Moreover, we will show that it preserves $2^{\aleph_1}=\aleph_2$.
