We introduce a new method for building models of $\mathsf{C}\mathsf{H}$, together with ${\mathrm{\Pi }}_2$ statements over $H({\omega }_2)$, by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only ${\aleph }_1$-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at ${\omega }_1$ known as $\mathsf{M}\mathsf{e}\mathsf{a}\mathsf{s}\mathsf{u}\mathsf{r}\mathsf{i}\mathsf{n}\mathsf{g}$ holds together with $\mathsf{C}\mathsf{H}$, thereby answering a well-known question of Moore. This construction can be described as a finite-support weak forcing iteration with side conditions consisting of suitable graphs of sets of models with markers. The $\mathsf{C}\mathsf{H}$-preservation is accomplished through the imposition of copying constraints on the information carried by the condition, as dictated by the edges in the graph.

我们引入了一种构建模型的新方法$\mathsf{C}\mathsf{H}$， 和...一起${\mathrm{\Pi }}_2$声明结束$H（{\omega }_2）$，通过强制。与文献中的其他强迫结构不同，我们的结构增加了新的实数，尽管只${\aleph }_1$-许多人。使用这种方法，我们建立了一个模型，其中对俱乐部猜测的否定的非常强的形式${\omega }_1$作为。。而被知道$\mathsf{中号}\mathsf{e}\mathsf{A}\mathsf{s}\mathsf{你}\mathsf{r}\mathsf{我}\mathsf{n}\mathsf{G}$结合在一起$\mathsf{C}\mathsf{H}$，从而回答了摩尔的一个著名问题。这种构造可以描述为有限支撑弱强迫迭代，其附带条件由带有标记的模型组的合适图组成。这$\mathsf{C}\mathsf{H}$- 保存是通过对条件所携带的信息施加复制约束来完成的，如图中的边所指示的。