联合钻石和紫菜钻石
Joint diamonds and Laver diamonds
摘要：
介绍了猜测原理的联合性概念，特别是$\diamondsuit_κ$和各种Laver钻石。一个猜测序列族是联合的，如果任何给定的目标序列的元素可以同时猜测的家庭的成员。虽然在$\diamondsuit_κ$的情况下是等价的，但联合Laver菱形是非平凡的新对象。我们给出了大多数考虑中的大基数的等同性结果，并证明了在$θ$ -超紧基数的情况下，不同长度的联合Laver金刚石之间的尖锐分离。
英文摘要：
The concept of jointness for guessing principles, specifically $\diamondsuit_κ$ and various Laver diamonds, is introduced. A family of guessing sequences is joint if the elements of any given sequence of targets may be simultaneously guessed by the members of the family. While equivalent in the case of $\diamondsuit_κ$, joint Laver diamonds are nontrivial new objects. We give equiconsistency results for most of the large cardinals under consideration and prove sharp separations between joint Laver diamonds of different lengths in the case of $θ$-supercompact cardinals.
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