Full Idea
There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories.
Clarification
'First-order' theories only refer to 'objects'
Gist of Idea
Model theory is mostly confined to first-order theories
Source
William D. Hart (The Evolution of Logic [2010], 9)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.236