# Set theory: Trending topics

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Rank Topic Wikipedia views
1 Set theory 2,742 2 Set (mathematics) 2,232 3 Cantor's diagonal argument 691 4 Total order 509 5 Naive set theory 422 6 Support (mathematics) 406 7 Multiplicity (mathematics) 314 8 Set-builder notation 303 9 Class (set theory) 265 10 Cantor's theorem 249 11 Set notation 244 12 Cardinality of the continuum 198 13 Mathematical structure 173 14 Goodstein's theorem 139 15 Controversy over Cantor's theory 120 16 Cantor's first uncountability proof 94 17 Extensionality 92 18 Almost 91 19 List of set theory topics 81 20 Paradoxes of set theory 74 21 Definable real number 73 22 Primitive notion 66 23 Transitive set 64 24 Continuum (set theory) 58 25 List of statements undecidable in ZFC 57 26 Reflection principle 57 27 Ordinal arithmetic 51 28 Tree (set theory) 48 29 Metamath 42 30 Hume's principle 39 31 Diamond principle 39 32 Set-theoretic topology 39 33 Ideal (set theory) 38 34 Equaliser (mathematics) 37 35 Solovay model 36 36 Stationary set 35 37 Fiber (mathematics) 35 38 Stratification (mathematics) 34 39 Hereditary set 33 40 Transitive reduction 31 41 Cofinality 30 42 Near sets 29 43 Infinitary combinatorics 27 44 Morass (set theory) 27 45 Vicious circle principle 26 46 Hereditarily finite set 25 47 Limit cardinal 25 48 Successor cardinal 24 49 Quasi-set theory 24 50 Pairing function 23 51 PCF theory 23 52 Diagonal intersection 23 53 Kuratowski's free set theorem 23 54 Ontological maximalism 22 55 Ω-logic 21 56 Normal function 19 57 Club set 17 58 Easton's theorem 17 59 Admissible set 17 60 Paradoxical set 17 61 Information diagram 17 62 Hartogs number 16 63 Ordinal definable set 16 64 Jónsson function 16 65 Scott's trick 16 66 Cardinal assignment 13 67 Continuous function (set theory) 13 68 Tail sequence 12 69 Recursive ordinal 11 70 Cabal (set theory) 10 71 Inductive set (axiom of infinity) 10 72 Suslin representation 9 73 Milner–Rado paradox 9 74 Separating set 8 75 Set-theoretic limit 7 76 Clubsuit 7 77 N-set 7 78 Fodor's lemma 7 79 Uniformization (set theory) 7 80 Global square 7 81 Set theory of the real line 7 82 Hereditarily countable set 7 83 Dimensional operator 7 84 Chang's conjecture 7 85 Club filter 6 86 Categorical set theory 6 87 Preordered class 6 88 Diaconescu's theorem less than 5 views
89 Mengenlehreuhr less than 5 views
90 Superstrong cardinal less than 5 views
91 Statements undecidable in ZFC less than 5 views
92 Set theory topics less than 5 views
93 Delta lemma less than 5 views
94 Exceptional set concepts less than 5 views
95 Code (set theory) less than 5 views
96 Laver function less than 5 views
97 Condensation lemma less than 5 views
98 Jensen's covering theorem less than 5 views
99 Soft set less than 5 views

# Encyclopedia

The main article for this category is Set theory.

Set theory is any of a number of subtly different things in mathematics:

• Naive set theory is the original set theory developed by mathematicians at the end of the 19th century, treating sets simply as collections of things.
• Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's paradox) in naive set theory. It treats sets as "whatever satisfies the axioms", and the notion of collections of things serves only as motivation for the axioms.
• Internal set theory is an axiomatic extension of set theory that supports a logically consistent identification of illimited (enormously large) and infinitesimal elements within the real numbers.
• Various versions of logic have associated sorts of sets (such as fuzzy sets in fuzzy logic).

## Subcategories

This category has the following 17 subcategories, out of 17 total.

## Pages in category "Set theory"

The following 108 pages are in this category, out of 108 total. This list may not reflect recent changes (learn more).

# Wiktionary

Up to date as of January 15, 2010

### Definition from Wiktionary, a free dictionary Articles on this topic in other Wikimedia projects can be found at: Wikimedia Commons Category Set theory Wikipedia has a category on:

Wikipedia

The following is a list of words related to set theory.

## Subcategories

This category has the following 8 subcategories, out of 8 total.

## Entries in category “Set theory”

The following 76 pages are in this category, out of 76 total.