论文标题
控制基本特征而无需添加实物
Controlling cardinal characteristics without adding reals
论文作者
论文摘要
我们研究了不增加新$ {<}κ$ - 序列（对于某些常规$κ$）的扩展条件下的真实元素的基本特征的行为。作为一个应用程序，我们表明以下基本特征可能会有所不同：Cichoń图中的（“独立”）特性，以及$ \ aleph_1 <\ alleph_1 <\ Mathfrak m <\ \ \ m athfrak p <\ mathfrak p <\ mathfrak h <\ mathrm {add}（add}（\ mathcal {n}）$。 （因此，我们获得了13个不同的值，包括$ \ aleph_1 $和Continuum）。我们还为单独的其他Ma-numbers（而不是$ \ Mathfrak M $）提供构造，即：Ma for Ma from Ma的$ K $ -KNASTER，以$ K+1 $ -KNASTER； MA和MA的所有$ K $ -KNASTER FOR MA的Precaliber for Precaliber。
We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new ${<}κ$-sequences (for some regular $κ$). As an application, we show that consistently the following cardinal characteristics can be different: The ("independent") characteristics in Cichoń's diagram, plus $\aleph_1<\mathfrak m<\mathfrak p<\mathfrak h<\mathrm{add}(\mathcal{N})$. (So we get thirteen different values, including $\aleph_1$ and continuum). We also give constructions to alternatively separate other MA-numbers (instead of $\mathfrak m$), namely: MA for $k$-Knaster from MA for $k+1$-Knaster; and MA for the union of all $k$-Knaster forcings from MA for precaliber.
