We consider the closure of three classical combination properties, namely, stable infiniteness, gentleness and shininess (or, equivalently for decidable theories, strong politeness), under intersection and combinability. We compute every possible intersection, and then compute the maximal set of theories that can be combined with each resulting intersection. We iterate this process until no new sets are identified. How many properties will we end up with?

翻译：我们研究了三种经典组合性质——稳定无穷性、温和性与光滑性（对于可判定理论等价于强礼貌性）——在交集与可组合性下的封闭性。我们计算了所有可能的交集，进而确定了能与每个所得交集进行组合的最大理论集合。我们迭代这一过程直至不再识别出新集合。最终我们将得到多少种性质？