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Mathematical logic has several meanings in common usage. It originally referred to symbolic or formal logic, and then came to be associated with the study of the logical (and even philosophical) foundations of mathematics. In contemporary use by mathematical logicians, the term refers to several branches of pure mathematics whose study involves careful attention to formal axiom systems and formal definability.

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.

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Mathematical logic