What is the Mathematical Logic?

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Topically, mathematical logic bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

Mathematical logic is often divided into the fields of Set theory, Model theory, Recursion theory, and Proof theory. These areas share basic results on logic, particularly first-order logic, and definability.