Mathematical Logic

https://en.wikipedia.org/wiki/Mathematical_logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, philosophy, 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 across the mathematical fields of

• set theory

• model theory

• recursion theory

• proof theory

These fields share basic results on logic, particularly first-order logic, and definability.