Reverse Mathematics
نویسنده
چکیده
In math we typically assume a set of axioms to prove a theorem. In reverse mathematics, the premise is reversed: we start with a theorem and try to determine the minimal axiomatic system required to prove the theorem (over a weak base system). This produces interesting results, as it can be shown that theorems from different fields of math such as group theory and analysis are in fact equivalent. Also, using reverse mathematics we can put theorems into a hierarchy by their complexity such that theorems that can be proven with weaker subsystems are “less complex”. This paper will introduce three frequently used subsystems of second-order arithmetic, give examples as to how different theorems would compare in a hierarchy of complexity, and culminate in a proof that subsystem ACA0 is equivalent to the statement that the range of every injective function exists.
منابع مشابه
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تاریخ انتشار 2010