We classify the Boolean degree $1$ functions of $k$-spaces in a vector space of dimension $n$ (also known as Cameron-Liebler classes) over the field with $q$ elements for $n \geq n_0(k, q)$. This also implies that two-intersecting sets with respect to $k$-spaces do not exist for $n \geq n_0(k, q)$. Our main ingredient is the Ramsey theory for geometric lattices.

翻译：我们对 $n$ 维向量空间中 $k$ 子空间上的布尔度 $1$ 函数（也称为 Cameron-Liebler 类）在域 $\mathbb{F}_q$ 上进行了分类，其中 $n \geq n_0(k, q)$。这也意味着对于 $n \geq n_0(k, q)$，关于 $k$ 子空间的二重相交集不存在。我们的主要工具是几何格上的拉姆齐理论。