Full Idea
Model theory helps one to understand what it takes to specify a mathematical structure uniquely.
Gist of Idea
Model theory reveals the structures of mathematics
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.1)
Book Reference
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.165
A Reaction
Thus it is the development of model theory which has led to the 'structuralist' view of mathematics.