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Universal set

In set theory, a universal set is a set that contains all of the objects in the theory, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory include a universal set.

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Overview

Reasons for nonexistence

Theories of universality

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Map overview Semantic statistics

Universal set

Nodes29
Edges28
Triples134
Avg. degree1.93
Density0.068966
Components1

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Universal set

Top relations

related to References · 95
Universal set → Alfred Tarski, Alonzo, Alonzo Church, American Mathematical Monthly, American Mathematical Society, An, An Introduction, Analyse, Andrew David, Anthony, Arnold, Berkeley, Cahiers, California, Center, Centre, Cenzer, Christopher, Church, Church's
related to Restricted comprehension · 13
Universal set → Alonzo Church, Another, Arnold Oberschelp, Church, In, New Foundations, Oberschelp's, Quine's, Such, The, There, Willard Van Orman Quine's, Zermelo's
related to External links · 7
Universal set → Bibliography, Eric, Forster, MathWorld, Randall Holmes, Set Theory, Weisstein
related to Universal objects that are not sets · 7
Universal set → Again, Fraenkel, It, One, Russell's, The, Zermelo
related to Cantor's theorem · 4
Universal set → Another, Because, Cantor's, However
related to Russell's paradox · 4
Universal set → If, Russell's, This, Zermelo's
related to Reasons for nonexistence · 2
Universal set → Many, There
is a · 1
Universal set → set that contains all of the objects in the theory
related to Theories of universality · 1
Universal set → The

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Important terminology

set universal theory sets axiom comprehension contain theories restricted displaystyle paradox russell's mr logic exist existence vol regularity pairing also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Universal setis aset that contains all of the objects in the theory0.90text
Universal setrelated to Cantor's theoremAnother0.60section
Universal setrelated to Cantor's theoremBecause0.60section
Universal setrelated to Cantor's theoremHowever0.60section
Universal setrelated to Cantor's theoremCantor's0.60section
Universal setrelated to External linksWeisstein0.60section
Universal setrelated to External linksEric0.60section
Universal setrelated to External linksMathWorld0.60section
Universal setrelated to External linksBibliography0.60section
Universal setrelated to External linksSet Theory0.60section
Universal setrelated to External linksForster0.60section
Universal setrelated to External linksRandall Holmes0.60section

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