Template: Set theory

{{Navbox
| name = Set theory
| state = {{{state|{{{1|<noinclude>un</noinclude>collapsed}}}}}}
| title = [[Set theory]]
| image = [[File:Venn A intersect B.svg|100px|link=Venn diagram|alt=Venn diagram of set intersection]]
| listclass = hlist

| group1 = Overview
| list1 =
* [[Set (mathematics)]]

<!------------------- Axioms -------------------->

| group2 = [[Axiom]]s
| list2 =
* [[Axiom of adjunction|Adjunction]]
* [[Axiom of choice|Choice]]
** [[Axiom of countable choice|countable]]
** [[Axiom of dependent choice|dependent]]
** [[Axiom of global choice|global]]
* [[Axiom of constructibility|Constructibility (V=L)]]
* [[Axiom of determinacy|Determinacy]]
* [[Axiom of extensionality|Extensionality]]
* [[Axiom of infinity|Infinity]]
* [[Axiom of limitation of size|Limitation of size]]
* [[Axiom of pairing|Pairing]]
* [[Axiom of power set|Power set]]
* [[Axiom of regularity|Regularity]]
* [[Axiom of union|Union]]
* [[Martin's axiom]]

* [[Axiom schema]]
** [[Axiom schema of replacement|replacement]]
** [[Axiom schema of specification|specification]]


<!----------------- Operations ------------------>

| group3 = [[Set (mathematics)#Basic operations|Operations]]
| list3 =
* [[Cartesian product]]
* [[Complement (set theory)|Complement]] (i.e. set difference)
* [[De Morgan's laws]]
* [[Disjoint union]]
* [[List of set identities and relations|Identities]]
* [[Intersection (set theory)|Intersection]]
* [[Power set]]
* [[Symmetric difference]]
* [[Union (set theory)|Union]]


<!------------- Concepts, methods --------------->

| group4 = {{hlist|Concepts|Methods}}
| list4 =
* [[Almost]]
* [[Cardinality]]
* [[Cardinal number]]&nbsp;([[Large cardinal|large]])
* [[Class (set theory)|Class]]
* [[Constructible universe]]
* [[Continuum hypothesis]]
* [[Cantor's diagonal argument|Diagonal argument]]
* [[Element (mathematics)|Element]]
** [[ordered pair]]
** [[tuple]]
* [[Family of sets|Family]]
* [[Forcing (mathematics)|Forcing]]
* [[Bijection|One-to-one correspondence]]
* [[Ordinal number]]
* [[Set-builder notation]]
* [[Transfinite induction]]
* [[Venn diagram]]


<!----------------- Set types ------------------->

| group5 = [[Set (mathematics)|Set]] types
| list5 =
* [[Amorphous set|Amorphous]]
* [[Countable set|Countable]]
* [[Empty set|Empty]]
* [[Finite set|Finite]]&nbsp;([[Hereditarily finite set|hereditarily]])
* [[Filter (set theory)|Filter]]
** [[Filter (set theory)|base]]
** [[Filter (set theory)#Filters and prefilters|subbase]]
** [[Ultrafilter on a set|Ultrafilter]]
* [[Fuzzy set|Fuzzy]]
* [[Infinite set|Infinite]] ([[Dedekind-infinite set|Dedekind-infinite]])
* [[Computable set|Recursive]]
* [[Singleton (mathematics)|Singleton]]
* [[Subset|Subset{{int:dot-separator}}Superset]]
* [[Transitive set|Transitive]]
* [[Uncountable set|Uncountable]]
* [[Universal set|Universal]]


<!------------------ Theories ------------------->

| group6 = Theories
| list6 =
* [[Alternative set theory|Alternative]]
* [[Set theory#Formalized set theory|Axiomatic]]
* [[Naive set theory|Naive]]
* [[Cantor's theorem]]

<!--(By derivation or/then chronology:)-->
* [[Zermelo set theory|Zermelo]]                                 <!--(1908)-->
** [[General set theory|General]]                                <!--(1998)-->
* ''[[Principia Mathematica]]''                                  <!--(1910s)--> 
** [[New Foundations|New Foundations<!--{{smaller|(NF, NFU)}}-->]] <!--(axiomatic, 1937/1960s)-->
* [[Zermelo–Fraenkel set theory|Zermelo–Fraenkel <!--{{smaller|(ZFC)}}-->]] <!--(axiomatic, 1920s)-->
** [[Von Neumann–Bernays–Gödel set theory|von Neumann–Bernays–Gödel <!--{{smaller|(NBG)}}-->]] <!--(axiomatic, 1920s–50s, conservative)-->
*** [[Morse–Kelley set theory|Morse–Kelley]]                     <!--(axiomatic, 1949–60s, non-conservative)-->
** [[Kripke–Platek set theory|Kripke–Platek]]                    <!--(axiomatic, 1960s)-->
** [[Tarski–Grothendieck set theory|Tarski–Grothendieck]]        <!--(axiomatic, 1980s?, non-conservative)-->


<!------------- Paradoxes, problems ------------->

| group7 = {{hlist|[[Paradoxes of set theory|Paradoxes]]|Problems}}
| list7 =
* [[Russell's paradox]]
* [[Suslin's problem]]
* [[Burali-Forti paradox]]


<!---------------- Set theorists ---------------->

| group8 = [[:Category:Set theorists|Set theorists]]
| list8 =
* [[Paul Bernays]]
* [[Georg Cantor]]
* [[Paul Cohen]]
* [[Richard Dedekind]]
* [[Abraham Fraenkel]]
* [[Kurt Gödel]]
<!--* [[Lorenz Halbeisen]]-->
* [[Thomas Jech]]
* [[John von Neumann]]
* [[Willard Van Orman Quine|Willard Quine]]
* [[Bertrand Russell]]
* [[Thoralf Skolem]]
* [[Ernst Zermelo]]


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