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Template:Set theory - Revision history
2026-05-14T05:30:08Z
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Kurt: 1 revision imported
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Kurt
https://www.thegoonshow.co.uk/wiki/index.php?title=Template:Set_theory&diff=3015&oldid=prev
en>SamanthaNguyen: + Set-builder notation
2022-01-10T02:02:43Z
<p>+ <a href="/wiki/index.php?title=Set-builder_notation&action=edit&redlink=1" class="new" title="Set-builder notation (page does not exist)">Set-builder notation</a></p>
<p><b>New page</b></p><div>{{Navbox<br />
| name = Set theory<br />
| state = {{{state|{{{1|<noinclude>un</noinclude>collapsed}}}}}}<br />
| title = [[Set theory]]<br />
| image = [[File:Venn A intersect B.svg|100px|link=Venn diagram|alt=Venn diagram of set intersection]]<br />
| listclass = hlist<br />
<br />
| group1 = Overview<br />
| list1 =<br />
* [[Set (mathematics)]]<br />
<br />
<!------------------- Axioms --------------------><br />
<br />
| group2 = [[Axiom]]s<br />
| list2 =<br />
* [[Axiom of adjunction|Adjunction]]<br />
* [[Axiom of choice|Choice]]<br />
** [[Axiom of countable choice|countable]]<br />
** [[Axiom of dependent choice|dependent]]<br />
** [[Axiom of global choice|global]]<br />
* [[Axiom of constructibility|Constructibility (V=L)]]<br />
* [[Axiom of determinacy|Determinacy]]<br />
* [[Axiom of extensionality|Extensionality]]<br />
* [[Axiom of infinity|Infinity]]<br />
* [[Axiom of limitation of size|Limitation of size]]<br />
* [[Axiom of pairing|Pairing]]<br />
* [[Axiom of power set|Power set]]<br />
* [[Axiom of regularity|Regularity]]<br />
* [[Axiom of union|Union]]<br />
* [[Martin's axiom]]<br />
<br />
* [[Axiom schema]]<br />
** [[Axiom schema of replacement|replacement]]<br />
** [[Axiom schema of specification|specification]]<br />
<br />
<br />
<!----------------- Operations ------------------><br />
<br />
| group3 = [[Set (mathematics)#Basic operations|Operations]]<br />
| list3 =<br />
* [[Cartesian product]]<br />
* [[Complement (set theory)|Complement]] (a.k.a set difference)<br />
* [[De Morgan's laws]]<br />
* [[Disjoint union]]<br />
* [[Intersection (set theory)|Intersection]]<br />
* [[Power set]]<br />
* [[Symmetric difference]]<br />
* [[Union (set theory)|Union]]<br />
<br />
<br />
<!------------- Concepts, methods ---------------><br />
<br />
| group4 = {{hlist|Concepts|Methods}}<br />
| list4 =<br />
* [[Cardinality]]<br />
* [[Cardinal number]]&nbsp;([[Large cardinal|large]])<br />
* [[Class (set theory)|Class]]<br />
* [[Constructible universe]]<br />
* [[Continuum hypothesis]]<br />
* [[Cantor's diagonal argument|Diagonal argument]]<br />
* [[Element (mathematics)|Element]]<br />
** [[ordered pair]]<br />
** [[tuple]]<br />
* [[Family of sets|Family]]<br />
* [[Forcing (mathematics)|Forcing]]<br />
* [[Bijection|One-to-one correspondence]]<br />
* [[Ordinal number]]<br />
* [[Set-builder notation]]<br />
* [[Transfinite induction]]<br />
* [[Venn diagram]]<br />
<br />
<br />
<!----------------- Set types -------------------><br />
<br />
| group5 = [[Set (mathematics)|Set]] types<br />
| list5 =<br />
* [[Amorphous set|Amorphous]]<br />
* [[Countable set|Countable]]<br />
* [[Empty set|Empty]]<br />
* [[Finite set|Finite]]&nbsp;([[Hereditarily finite set|hereditarily]])<br />
* [[Fuzzy set|Fuzzy]]<br />
* [[Infinite set|Infinite]] ([[Dedekind-infinite set|Dedekind-infinite]])<br />
* [[Recursive set|Recursive]]<br />
* [[Singleton (mathematics)|Singleton]]<br />
* [[Subset and superset|Subset{{int:dot-separator}}Superset]]<br />
* [[Transitive set|Transitive]]<br />
* [[Uncountable set|Uncountable]]<br />
* [[Universal set|Universal]]<br />
<br />
<br />
<!------------------ Theories -------------------><br />
<br />
| group6 = Theories<br />
| list6 =<br />
* [[Alternative set theory|Alternative]]<br />
* [[Axiomatic set theory|Axiomatic]]<br />
* [[Naive set theory|Naive]]<br />
* [[Cantor's theorem]]<br />
<br />
<!--(By derivation or/then chronology:)--><br />
* [[Zermelo set theory|Zermelo]] <!--(1908)--><br />
** [[General set theory|General]] <!--(1998)--><br />
* ''[[Principia Mathematica]]'' <!--(1910s)--> <br />
** [[New Foundations|New Foundations<!--{{smaller|(NF, NFU)}}-->]] <!--(axiomatic, 1937/1960s)--><br />
* [[Zermelo–Fraenkel set theory|Zermelo–Fraenkel <!--{{smaller|(ZFC)}}-->]] <!--(axiomatic, 1920s)--><br />
** [[Von Neumann–Bernays–Gödel set theory|von Neumann–Bernays–Gödel <!--{{smaller|(NBG)}}-->]] <!--(axiomatic, 1920s–50s, conservative)--><br />
*** [[Morse–Kelley set theory|Morse–Kelley]] <!--(axiomatic, 1949–60s, non-conservative)--><br />
** [[Kripke–Platek set theory|Kripke–Platek]] <!--(axiomatic, 1960s)--><br />
** [[Tarski–Grothendieck set theory|Tarski–Grothendieck]] <!--(axiomatic, 1980s?, non-conservative)--><br />
<br />
<br />
<!------------- Paradoxes, problems -------------><br />
<br />
| group7 = {{hlist|[[Paradoxes of set theory|Paradoxes]]|Problems}}<br />
| list7 =<br />
* [[Russell's paradox]]<br />
* [[Suslin's problem]]<br />
* [[Burali-Forti paradox]]<br />
<br />
<br />
<!---------------- Set theorists ----------------><br />
<br />
| group8 = [[:Category:Set theorists|Set theorists]]<br />
| list8 =<br />
* [[Abraham Fraenkel]]<br />
* [[Bertrand Russell]]<br />
* [[Ernst Zermelo]]<br />
* [[Georg Cantor]]<br />
* [[John von Neumann]]<br />
* [[Kurt Gödel]]<br />
* [[Paul Bernays]]<br />
* [[Paul Cohen]]<br />
* [[Richard Dedekind]]<br />
* [[Thomas Jech]]<br />
* [[Thoralf Skolem]]<br />
* [[Willard Van Orman Quine|Willard Quine]]<br />
<br />
<br />
}}<noinclude><br />
{{Documentation<br />
| content =<br />
{{Collapsible option |statename=optional |default=collapsed}}<br />
<br />
{{Logic templates}}<br />
<br />
[[Category:Logic templates]]<br />
[[Category:Mathematics navigational boxes]]<br />
}}<!--(end Documentation)--><br />
</noinclude></div>
en>SamanthaNguyen