Difference between revisions of "Template:Mathematical logic"

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imported>JP.Martin-Flatin
(Added Map, Relation, and Infinite set to Group 5 and renamed that group "Naive set theory". Created group 6 "Set theory".)
imported>Sardanaphalus
(state handling; merged groups 5,6; subgroups (list1,5); moved Foundations link (most general) to "below" line; subheading+link now covered by template (Documentation))
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{{Navbox
 
{{Navbox
 
| name = Mathematical logic
 
| name = Mathematical logic
| state = {{{state|autocollapse}}}
+
| state = {{{state|{{{1|<noinclude>expanded</noinclude>}}}}}}
 
| title = [[Mathematical logic]]
 
| title = [[Mathematical logic]]
 
| listclass = hlist
 
| listclass = hlist
| image=
 
  
  | group1 = General
+
| group1 = General
   | list1 =
+
| list1 =
* [[Formal language]]
+
   {{Navbox |child |groupstyle=font-weight:normal;
 +
  | list1 = <!--(Alphabetical (by label):)-->
 +
* [[Axiom]]
 +
* [[Class (set theory)|Class]]
 +
* [[Element (mathematics)|Element]]
 
* [[Formation rule]]
 
* [[Formation rule]]
* [[Formal system]]
+
* [[Logical consequence]]
* [[Deductive system]]
 
* [[Formal proof]]
 
* [[Formal semantics (logic)|Formal semantics]]
 
* [[Well-formed formula]]
 
* [[Set (mathematics)|Set]]
 
* [[Element (mathematics)|Element]]
 
* [[Class (set theory)|Class]]
 
* [[Classical logic]]
 
* [[Axiom]]
 
 
* [[Natural deduction]]
 
* [[Natural deduction]]
 +
* [[Finitary relation|Relation]]
 
* [[Rule of inference]]
 
* [[Rule of inference]]
* [[Finitary relation|Relation]]
+
* [[Set (mathematics)|Set]]
* [[Theorem]]
 
* [[Logical consequence]]
 
* [[Axiomatic system]]
 
* [[Type theory]]
 
 
* [[Symbol (formal)|Symbol]]
 
* [[Symbol (formal)|Symbol]]
 
* [[Syntax (logic)|Syntax]]
 
* [[Syntax (logic)|Syntax]]
 +
* [[Theorem]]
 
* [[Theory (mathematical logic)|Theory]]
 
* [[Theory (mathematical logic)|Theory]]
 +
* [[Type theory]]
 +
* [[Well-formed formula]]
 +
  | group2 = Systems
 +
  | list2 =
 +
* [[Axiomatic system|Axiomatic]]
 +
* [[Classical logic|Classical]]
 +
* [[Deductive system|Deductive]]
 +
* [[Formal system|Formal]]
 +
** [[Formal language|language]]
 +
** [[Formal proof|proof]]
 +
** [[Formal semantics (logic)|semantics]]
 +
  }}
  
  | group2 = [[Term logic|Traditional logic]]
+
<!---group2 omitted to maintain alternating list backgrounds--->
  | list2 =
+
 
 +
| group3 = [[Term logic|Traditional logic]]
 +
| list3 =
 
* [[Proposition]]
 
* [[Proposition]]
 
* [[Inference]]
 
* [[Inference]]
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* [[Venn diagram]]
 
* [[Venn diagram]]
  
  | group3 = {{longitem|[[Propositional calculus|Propositional <br/>calculus]]<br/>[[Boolean algebra|Boolean logic]]}}
+
| group4 = [[Propositional calculus]]<br/>[[Boolean algebra|Boolean logic]]
  | list3 =
+
| list4 =
 
* [[Boolean function]]s
 
* [[Boolean function]]s
* [[Propositional calculus]]
 
 
* [[Propositional formula]]
 
* [[Propositional formula]]
 
* [[Logical connective]]s
 
* [[Logical connective]]s
 
* [[Truth table]]s
 
* [[Truth table]]s
  
  | group4 = [[Predicate logic]]
+
| group5 = [[Predicate logic]]
  | list4 =
+
| list5 =
 
* [[First-order logic|First-order]]
 
* [[First-order logic|First-order]]
 
* [[Quantifier (logic)|Quantifiers]]
 
* [[Quantifier (logic)|Quantifiers]]
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* [[Monadic predicate calculus]]
 
* [[Monadic predicate calculus]]
  
  | group5 = [[Naive set theory]]
+
<!----------------------------------------------------------------------------->
   | list5 =
+
| group6 = [[Set theory]]
* [[Set (mathematics)|Set]]
+
| list6 =
* [[Empty set]]
+
   {{Navbox |child |groupstyle=font-weight:normal;
 +
 
 +
  | group1 = [[Naive set theory|Naive]]
 +
  | list1 =
 +
    {{Navbox |child |groupstyle=font-weight:normal; |evenodd=swap
 +
      | list1 =
 +
* [[Domain of a function|Domain]]
 
* [[Enumeration]]
 
* [[Enumeration]]
 
* [[Extensionality]]
 
* [[Extensionality]]
* [[Finite set]]
+
* [[Function (mathematics)|Function]]
* [[Infinite set]]
+
* [[Map (mathematics)|Map]]
* [[Subset]]
+
* [[Ordered pair]]
* [[Power set]]
 
* [[Countable set]]
 
* [[Uncountable set]]
 
* [[Recursive set]]
 
* [[Domain of a function|Domain]]
 
 
* [[Range (mathematics)|Range]]
 
* [[Range (mathematics)|Range]]
* [[Map (mathematics)|Map]]
 
* [[Function (mathematics)|Function]]
 
 
* [[Binary operation|Relation]]
 
* [[Binary operation|Relation]]
* [[Ordered pair]]
+
      | group2 = [[Set (mathematics)|Set]] types
 +
      | list2 =
 +
* [[Countable set|Countable]]
 +
* [[Empty set|Empty]]
 +
* [[Finite set|Finite]]
 +
* [[Infinite set|Infinite]]
 +
* [[Power set|Power]]
 +
* [[Recursive set|Recursive]]
 +
* [[Subset]]
 +
* [[Uncountable set|Uncountable]]
 +
    }}
  
  | group6 = [[Set theory]]
+
  | group2 = Formal
  | list6 =
+
  | list2 =
* [[Foundations of mathematics]]
+
    {{Navbox |child |groupstyle=font-weight:normal; |evenodd=swap
* [[Zermelo–Fraenkel set theory]]
+
    | list1 =
 
* [[Axiom of choice]]
 
* [[Axiom of choice]]
* [[General set theory]]
+
    | group2 = Theories
* [[Kripke–Platek set theory]]
+
    | list2 = <!--(by derivation or/then chronology:)-->
* [[Von Neumann–Bernays–Gödel set theory]]
+
* [[Zermelo set theory|Zermelo]]                                      <!--(1908)-->
* [[Morse–Kelley set theory]]
+
** [[General set theory|General]]                                     <!--(1998)-->
* [[Tarski–Grothendieck set theory]]
+
* [[Zermelo–Fraenkel set theory|Zermelo–Fraenkel]]                   <!--(axiomatic, 1920s)-->
 +
** [[Von Neumann–Bernays–Gödel set theory|von Neumann–Bernays–Gödel]] <!--(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)-->
 +
}} }}
 +
<!----------------------------------------------------------------------------->
 +
 
 +
<!---group7 omitted to maintain alternating list backgrounds--->
  
  | group7 = [[Model theory]]
+
| group8 = [[Model theory]]
  | list7 =
+
| list8 =
 
* [[Structure (mathematical logic)|Model]]
 
* [[Structure (mathematical logic)|Model]]
 
* [[Interpretation (logic)|Interpretation]]
 
* [[Interpretation (logic)|Interpretation]]
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* [[Validity]]
 
* [[Validity]]
  
  | group8 = [[Proof theory]]
+
| group9 = [[Proof theory]]
  | list8 =
+
| list9 =
 
* [[Formal proof]]
 
* [[Formal proof]]
 
* [[Deductive system]]
 
* [[Deductive system]]
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* [[Syntax (logic)|Syntax]]
 
* [[Syntax (logic)|Syntax]]
  
  | group9 = [[Computability theory|Computability <br/>theory]]
+
| group10 = [[Computability theory]]
  | list9 =
+
| list10 =
 
* [[Recursion]]
 
* [[Recursion]]
 
* [[Recursive set]]
 
* [[Recursive set]]
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* [[Primitive recursive function]]
 
* [[Primitive recursive function]]
  
<!--| below = ...-->
+
| below = [[Foundations of mathematics]]
 +
 
 
}}<noinclude>
 
}}<noinclude>
{{documentation|content=
+
{{Documentation
{{collapsible option}}
+
| content =
 +
{{Collapsible option |statename=optional}}
  
==See also==
 
*{{tl|Set theory}}
 
 
{{Logic templates}}
 
{{Logic templates}}
  
 
[[Category:Mathematics navigational boxes]]
 
[[Category:Mathematics navigational boxes]]
 
[[Category:Philosophy and thinking navigational boxes]]
 
[[Category:Philosophy and thinking navigational boxes]]
 
+
}}<!--(end Documentation)-->
}}
 
 
</noinclude>
 
</noinclude>

Revision as of 20:07, 27 November 2014

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