Axiomatic Views of Aggregates
In undertaking the first axiomatization of set theory, around 1908, Zermelo could refer simply to “set theory as it is historically given.” Today one must distinguish between set theory, which is a wide and varied panorama, and several set languages embellishing the landscape, that have arisen in part from epistemological, in part from practical motivations. The meaning of such languages is often provided by a system of axioms, subject to the deductive machinery of firstorder logic.
KeywordsTransitive Closure Axiomatic System Peano Arithmetic Membership Relation Boolean Ring
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