Help understanding the definition of positive semidefinite matrix

Please confirm or deny the correctness of my understanding about this definition.

For a given set of ##t_i##s, the matrix ##(B(t_i,t_j))^k_{i,j=1}## is a constant ##k\times k## matrix, whose entries are given by ##B(t_i,t_j)## for each ##i## and ##j##.

The the 'finite' in the last line of the definition refers to ##t_1## and ##t_k## is finite, and ##k## is assumed to be a finite integer.

And if we impose the condition ##t_1<t_2<...<t_k## , then for all finite time slices' ##\{t_i\}_{i=1}^k## means ##\{t_1,...,t_k | (t_1<t_2<...<t_k) \text{ and } (t_i
\in \mathbb{R} \text{ for all } i \in \{1,...,k\}) \text{ and } (-\infty < t_1 < t_k < \infty)\}.##

One such ' time slice' is ##1,2,3,...k##. Another is ##-1,-,\frac{1}{2},...,-\frac{1}{k-1},-\frac{1}{k}.##


A few questions I have are, what information does ##\{t_i\}^k_{i=1}## convey? I find interpreting this notation confusing. Is 'time slice' a precise term at all?

Thank you.

To add, if someone defines the function ##B## as ##B(s,t)=\mathbb{E}[X_sX_t]##, the matrix ##((B(i,j))_{i,j=1}^k)=M## is symmetric, i.e., ##M_{ij}=M_{ji}=\mathbb{E}[X_sX_t]= \mathbb{E}[X_tX_s].##