Full Idea
In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these.
Clarification
'isomorphic' means maps onto
Gist of Idea
We only need to study mathematical models, since all other models are isomorphic to these
Source
John P. Burgess (Philosophical Logic [2009], 1.8)
Book Reference
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.10
A Reaction
The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered.