Full Idea
Tarski invoked the notion of a sentential function, where components are replaced by appropriate variables. A function is then satisfied by assigning objects to variables. An assignment satisfies if the function is true of the things assigned.
Gist of Idea
Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them
Source
report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Ian Rumfitt - The Boundary Stones of Thought 3.2
Book Reference
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.72
A Reaction
[very compressed] This use of sentential functions, rather than sentences, looks like the key to Tarski's definition of truth.