Consider the following definitions for statistical model
In mathematical terms, a statistical model is usually thought of as a pair $(S,P)$, where $S$ is the set of possible observations, i.e. the sample space, and $P$ is a set of probability distributions on $S$.
A statistical model $\mathfrak{F}$ is a set of distributions (or densities or regression functions).
And I noticed that several textbooks used the word statistical model bypassing the actual definition.
I have the following doubt
1) Is it an ordered pair or a set as per formal definition?
It hardly makes a difference.
Technically the answer is that it is an ordered pair of a set $S$ and a set $P$ of probabilit distributions on $S$. However, when specifying the set $P$, one has to make a choice of a base set $S$ anyway. Hence one implicitely chooses a set.
To give another example, one may (and usually does) define a topological space as an ordered pair consisting of a set $X$ and a topology $\tau \subseteq \wp(X)$. However, one may informally say that "a topological space is a set of subsets such that ...", where in the definition of the topology the base set is included.
Again, it hardly makes a difference. Whats important is that one needs to specify a set $S$ and a set $P$ of probability distributions. How that is done is conventional.