Difference between revisions of "First-order language"
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First-order languages are used to describe [[mathematics]] in [[mathematical notation]] with [[mathematical formula]]e. | First-order languages are used to describe [[mathematics]] in [[mathematical notation]] with [[mathematical formula]]e. | ||
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Revision as of 21:28, December 3, 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.
