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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of deriving theorems from axioms. The reverse mathematics program was foreshadowed by results in set theory such as the classical theorem that the axiom of choice and Zorn''s lemma are equivalent over ZF set theory. The goal of reverse mathematics, however, is to study ordinary theorems of mathematics rather than possible axioms for set theory.