Mathematical logic

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Mathematical logic is the study of logic within mathematics. This is commonly done by means of formal systems called formal logics that define rules of reasoning and the axioms they satisfy. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include usage of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of the foundations of mathematics. This study began in the late 19th century for resolving the foundational crisis of mathematics. In the early 20th century David Hilbert's proposed a program to resolve the crisis, and in particular to prove the consistency of mathematics. Results of Kurt Gödel, Gerhard Gentzen...

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