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Set Theory (Stanford Encyclopedia of Philosophy)

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Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. Pure set theory deals exclusively with sets, so the only sets under consideration are those whose members are also sets. The theory of the hereditarily-finite sets, namely those finite sets whose elements are also finite sets, the elements of which are also finite, and so on, is formally equivalent to arithmetic. So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite. The notion of set is so simple that it is usually introduced informally, and regarded as self-evident. In set theory, however, as is usual in mathematics, sets are given axiomatically, so their existence and basic properties are postulated by the appropriate formal axioms. The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathemati

--> Set Theory (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy Menu Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Navigation Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top Set Theory First published Wed Oct 8, 2014; substantive revision Tue Jan 31, 2023 Set theory is the mathematical

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