As everyone knows, forcing was created by Cohen to answer questions in set theory.
Question 1. What are the first applications of set theoretic forcing in other branches of mathematical logic, like number theory, computability theory, complexity theory and model theory.
Question 2. What are the first applications of set theoretic forcing in other branches of mathematics like topology, algebra, analysis, ....
Update. Here I will collect the answers and will add a few that I am aware:
1) Scott, "A proof of the independence of the continuum hypothesis": models of higher order theories of the Real numbers.
2) Feferman, "Some applications of the notions of forcing and generic sets": Number theory.
3) Abraham Robinson, "Forcing in model theory" : Model theory.
4) Fernando Tohmè, Gianluca Caterina, Rocco Gangle, "Forcing Iterated Admissibility in Strategic Belief Models": Game theory (in particular epistemic game theory).
5) Solovay, Tennenbaum, "Iterated Cohen extensions and Souslin's problem" : Analysis-Topology.
6) Shelah, "Infinite abelian groups, Whitehead problem and some constructions" : Algebra.
What about "Recursion theory" and "Complexity theory"?