**Set theory** is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.

The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.

Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.

Read more about Set Theory: History, Basic Concepts, Some Ontology, Axiomatic Set Theory, Applications, Objections To Set Theory As A Foundation For Mathematics

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**set Theory**)

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**set**W in V which is a standard model of ZF, and the ordinal κ is the

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**Set Theory**

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**set theory**is a collection of nested axiomatic

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**Set Theory**As A Foundation For Mathematics

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**set theory**, introduces into mathematics methods and objects that are not computable even in ...

... Levy A hierarchy of formulas in

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**Set Theory**, Symposia Pure Math ... Levy Basic

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### Famous quotes containing the words theory and/or set:

“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical *theory* will abandon that point of view.”

—Thomas Nagel (b. 1938)

“O, he’s drunk, Sir Toby, an hour agone; his eyes were *set* at eight i’ th’ morning.”

—William Shakespeare (1564–1616)