This is a problem from Introduction to Mathematical Logic course
A structure $\mathscr{A}$ with domain $\mathbb{N}^k$ is for FOL language $\mathscr{L}$ with $k$ predicate symbols $p_1, \ldots, p_k$ that all have two arguments and are interpreted as follow: $(a,b)\in p_i \Leftrightarrow a_i \leq b_i$ where $a_i$ and $b_i$ are the $i$-th components of $a$ and $b$.
Suggest a formula that describes the set $\{(x,x,\ldots,x)\in \mathbb{N}^k : x\in \mathbb{N}\}$.
Clearly every element of the domain $(a_1,\ldots,a_k)$ can be described with formula. You can describe the sets with $i$-th component $a_i$ and then you can describe the intersection of these sets.
What about the case in the question?