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| | + | | state = {{{state|{{{1|<noinclude>expanded</noinclude>}}}}}} |
| title = [[Mathematical logic]] | | title = [[Mathematical logic]] | ||
| listclass = hlist | | listclass = hlist | ||
| − | |||
| − | + | | group1 = General | |
| − | | list1 = | + | | list1 = |
| − | * [[ | + | {{Navbox |child |groupstyle=font-weight:normal; |
| + | | list1 = <!--(Alphabetical (by label):)--> | ||
| + | * [[Axiom]] | ||
| + | * [[Class (set theory)|Class]] | ||
| + | * [[Element (mathematics)|Element]] | ||
* [[Formation rule]] | * [[Formation rule]] | ||
| − | * [[ | + | * [[Logical consequence]] |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
* [[Natural deduction]] | * [[Natural deduction]] | ||
| + | * [[Finitary relation|Relation]] | ||
* [[Rule of inference]] | * [[Rule of inference]] | ||
| − | * [[ | + | * [[Set (mathematics)|Set]] |
| − | |||
| − | |||
| − | |||
| − | |||
* [[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 omitted to maintain alternating list backgrounds---> | |
| − | + | ||
| + | | group3 = [[Term logic|Traditional logic]] | ||
| + | | list3 = | ||
* [[Proposition]] | * [[Proposition]] | ||
* [[Inference]] | * [[Inference]] | ||
| Line 42: | Line 48: | ||
* [[Venn diagram]] | * [[Venn diagram]] | ||
| − | + | | group4 = [[Propositional calculus]]<br/>[[Boolean algebra|Boolean logic]] | |
| − | + | | list4 = | |
* [[Boolean function]]s | * [[Boolean function]]s | ||
| − | |||
* [[Propositional formula]] | * [[Propositional formula]] | ||
* [[Logical connective]]s | * [[Logical connective]]s | ||
* [[Truth table]]s | * [[Truth table]]s | ||
| − | + | | group5 = [[Predicate logic]] | |
| − | + | | list5 = | |
* [[First-order logic|First-order]] | * [[First-order logic|First-order]] | ||
* [[Quantifier (logic)|Quantifiers]] | * [[Quantifier (logic)|Quantifiers]] | ||
| Line 58: | Line 63: | ||
* [[Monadic predicate calculus]] | * [[Monadic predicate calculus]] | ||
| − | + | <!-----------------------------------------------------------------------------> | |
| − | | | + | | group6 = [[Set theory]] |
| − | + | | list6 = | |
| − | * [[ | + | {{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]] | ||
| − | * [[ | + | * [[Function (mathematics)|Function]] |
| − | * [[ | + | * [[Map (mathematics)|Map]] |
| − | * [[ | + | * [[Ordered pair]] |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
* [[Range (mathematics)|Range]] | * [[Range (mathematics)|Range]] | ||
| − | |||
| − | |||
* [[Binary operation|Relation]] | * [[Binary operation|Relation]] | ||
| − | * [[ | + | | 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]] | ||
| + | }} | ||
| − | + | | group2 = Formal | |
| − | + | | list2 = | |
| − | + | {{Navbox |child |groupstyle=font-weight:normal; |evenodd=swap | |
| − | + | | list1 = | |
* [[Axiom of choice]] | * [[Axiom of choice]] | ||
| − | * [[General set theory]] | + | | group2 = Theories |
| − | * [[ | + | | 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---> | ||
| − | + | | group8 = [[Model theory]] | |
| − | + | | list8 = | |
* [[Structure (mathematical logic)|Model]] | * [[Structure (mathematical logic)|Model]] | ||
* [[Interpretation (logic)|Interpretation]] | * [[Interpretation (logic)|Interpretation]] | ||
| Line 98: | Line 120: | ||
* [[Validity]] | * [[Validity]] | ||
| − | + | | group9 = [[Proof theory]] | |
| − | + | | list9 = | |
* [[Formal proof]] | * [[Formal proof]] | ||
* [[Deductive system]] | * [[Deductive system]] | ||
| Line 108: | Line 130: | ||
* [[Syntax (logic)|Syntax]] | * [[Syntax (logic)|Syntax]] | ||
| − | + | | group10 = [[Computability theory]] | |
| − | + | | list10 = | |
* [[Recursion]] | * [[Recursion]] | ||
* [[Recursive set]] | * [[Recursive set]] | ||
| Line 118: | Line 140: | ||
* [[Primitive recursive function]] | * [[Primitive recursive function]] | ||
| − | + | | below = [[Foundations of mathematics]] | |
| + | |||
}}<noinclude> | }}<noinclude> | ||
| − | {{ | + | {{Documentation |
| − | {{ | + | | content = |
| + | {{Collapsible option |statename=optional}} | ||
| − | |||
| − | |||
{{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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