Full Idea
The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all.
Gist of Idea
Modern model theory begins with the proof of Los's Conjecture in 1962
Source
William D. Hart (The Evolution of Logic [2010], 9)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.238