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Set theory

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.

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Overview

History

Basic concepts and notation

Ontology

Formalized set theory

Applications

Areas of study

Relationships to other areas of mathematics

Controversy

Mathematical education

Bibliography

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Set theory

Nodes253
Edges252
Triples295
Avg. degree1.99
Density0.007905
Components1

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Set theory

Top relations

related to References · 48
Set theory → Akihiro, An Historical Introduction, Berlin, Boston, Cantor's Paradise, Contemporary Set Theory, Continuum Problem, Critical Introduction, Devlin, Donald, Dover Publications, Fitting, Fundamentals, Georg Cantor, Harvard University Press, History, Ideas, Infinite, Introduction, ISBN
related to External links · 43
Set theory → Akihiro, Assaf Rinot, Axiomatic, Basel, Birkhäuser, Choice, Daniel, Determinacy, Edward, EMS Press, Encyclopedia, Eric, Fraenkel, Handbook, History, Internet Encyclopedia, ISBN, Its Role, Joan, John
related to Naive set theory · 35
Set theory → All Real Algebraic Numbers, Arial Unicode MS, Cantor, Cantor's, Cardo, Code2000, Collection, DejaVu Sans, DejaVu Serif, EB Garamond, Foulis Greek, FreeSans, FreeSerif, Garamond, Garamond Libre, Gentium Book Plus, Gentium Plus, Georg Cantor, Greek, He
related to history · 24
Set theory → BC, Before, Bernard Bolzano's Paradoxes, Carl Friedrich Gauss, CE, East, Elea, Galileo's, Greek, History, However, In, Indian, Infinite, Infinity, Paradoxien, Porphyry, Since, The, Tree
related to Bibliography · 17
Set theory → Akihiro Kanamori, Google BooksMatthew Foreman, Handbook, ISBN, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Naive Set Theory, Online, Paul Halmos, Print, Set, Springer, Springer Verlag, The Third Millennium Edition, Thomas Jech, Wikisource-logo
related to Controversy · 11
Set theory → Constructive Analysis, Errett Bishop's, Foundations, Fraenkel, From, Henri Poincaré, If, Kronecker, Solomon Feferman, The, Zermelo
related to Inner model theory · 10
Set theory → An, Even, For, Fraenkel, Gödel, One, The, Thus, Zermelo, ZF
related to Descriptive set theory · 9
Set theory → Borel, Descriptive, In, It, Many, Polish, The, Wadge, ZFC
related to Basic concepts and notation · 8
Set theory → Also, As, For, If, More, Set, Since, We
related to Formalized set theory · 8
Set theory → Axiomatic, Burali-Forti, Elementary, Russell's, Such, The, This, Venn

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Important terminology

set theory sets mathematics mathematical example objects numbers axiom choice study model real infinity also many axioms cantor systems zermelo

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Set theoryis abranch of mathematical logic that studies sets0.90text
Set theoryis astudy of subsets of the real line and0.90text
Set theoryis afoundation for describing collections of mathematical objects0.90text
Leopold Kroneckerinstance ofThis caused it to encounter resistance from mathematical contemporaries0.80text
Henri Poincaréinstance ofThis caused it to encounter resistance from mathematical contemporaries0.80text
later from Hermann Weylinstance ofThis caused it to encounter resistance from mathematical contemporaries0.80text
Linstance ofThis caused it to encounter resistance from mathematical contemporaries0.80text
the projective hierarchyinstance ofIt begins with the study of pointclasses in the Borel hierarchy and extends to the study of more complex hierarchies0.80text
the Wadge hierarchyinstance ofIt begins with the study of pointclasses in the Borel hierarchy and extends to the study of more complex hierarchies0.80text
0.75.Inner model theoryAn inner model of Zermeloinstance ofis more flexible than a simple yes or no answer and can be a real number0.80text
the axiom of determinacy that contradict the axiom of choiceinstance ofespecially when considering axioms0.80text
0.75instance ofis more flexible than a simple yes or no answer and can be a real number0.80text

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