论文标题
Borel色度数字的本地可计数$F_σ$图形并用超级完美树强迫
Borel chromatic numbers of locally countable $F_σ$ graphs and forcing with superperfect trees
论文作者
论文摘要
在这项工作中，我们研究了由Geschke（2011）定义为连续体的基本特征的无数borel色数，低复杂度图。我们表明，具有紧凑的完全断开顶点的局部可计数图的强烈形式具有由borel色的数字，该数字在通过添加$ \ aleph_2 $ laver reals获得的模型中，由接地模型的连续体界定。由此，我们回答了Geschke和第二作者（2022）的问题，以及Fisher，Friedman和Khomskii（2014）的另一个问题，即真实行的子集的规律性属性。
In this work we study the uncountable Borel chromatic numbers, defined by Geschke (2011) as cardinal characteristics of the continuum, of low complexity graphs. We show that a strong form of locally countable graphs with compact totally disconnected set of vertices have Borel chromatic number bounded by the continuum of the ground model in the model obtained by adding $\aleph_2$ Laver reals. From this, we answer a question from Geschke and the second author (2022), and another question from Fisher, Friedman and Khomskii (2014) concerning regularity properties of subsets of the real line.
