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Mathematical Logic is a branch of mathematics that studies mathematical reasoning and argumentation through rigorous, formal systems. It's concerned with defining precisely what it means for statements in these systems to be true or false, and exploring how those statements can be combined and transformed according to specific rules. As part of Pure Mathematics within the broader context of Science and Mathematics, Mathematical Logic is fundamental to understanding the foundations of mathematics itself, as well as having applications in computer science, artificial intelligence, and linguistics. It deals with concepts such as proof theory, model theory, recursion theory, and set theory, providing a framework for formalizing mathematical reasoning and enabling the rigorous analysis of algorithms and computational systems. Overall, Mathematical Logic is a crucial tool for understanding the nature of mathematics, its limits, and its power in describing the world around us.