Difference between revisions of "First-order language"
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| − | A '''First-order language''' consists of the following symbols: | + | A '''First-order language''' in [[Zermelo-Fraenkel]] set theory consists of the following symbols: |
| − | #A set of | + | #A set of [[constant]]s, such as ''A'', ''B'', ''C'', ... |
| − | #A set of n-ary | + | #A set of n-ary [[relation]]s such as ''>(x, y)''. |
| − | #A set of n-ary | + | #A set of n-ary [[function]]s such as ''+(x, y)''. |
#An [[infinite]] set of variables such as ''x'', ''y'', ''z'',... | #An [[infinite]] set of variables such as ''x'', ''y'', ''z'',... | ||
#The connectives <math>\neg</math>, <math>\wedge</math>. | #The connectives <math>\neg</math>, <math>\wedge</math>. | ||
| − | # | + | #[[quantifier]]s: <math>\forall</math>, <math>\exists</math>. |
#parenthesis: <math>(</math>, <math>)</math>. | #parenthesis: <math>(</math>, <math>)</math>. | ||
| − | #The equality symbol <math>=</math>. | + | #The [[equality]] symbol <math>=</math>. |
| + | |||
| + | First-order languages are used to describe [[mathematics]] in [[mathematical notation]] with [[mathematical formula]]e. | ||
[[category:languages]] | [[category:languages]] | ||
| + | [[category:logic]] | ||
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 00:22, March 9, 2008
A First-order language in Zermelo-Fraenkel set theory consists of the following symbols:
- A set of constants, such as A, B, C, ...
- A set of n-ary relations such as >(x, y).
- A set of n-ary functions such as +(x, y).
- An infinite set of variables such as x, y, z,...
- The connectives
, 
. - quantifiers:
, 
. - parenthesis:
, 
. - The equality symbol
.
First-order languages are used to describe mathematics in mathematical notation with mathematical formulae.
