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Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
Mathematical logic is divided into four parts:
- Model theory
- Proof theory
- Recursion theory, also known as computability theory
- Set theory
The divisions between these areas, along with the divisions between mathematical logic and the rest of mathematics, are not completely sharp, with many areas of research and methods overlapping and reinforcing each other.