Classification theory, forking, type: naming of a set of variables

Question

In the snippet below which is taken from the Shelah's book Classification Theory, what does $U$ in $$\bar{x}_U$$ stand for; why was it named so ? What type of object is $U$ ?

Answer 1

He explains the notation literally a few lines above that at the start of the section. The $U$ here is just an index set. I don't know why he chooses that name.

So what it means is that $\bar{x}_U$ is just a tuple of variables, and for each $k$ we have a subtuple, denoted by $\bar{x}^k$.