First-order language

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A First-order language in Zermelo-Fraenkel set theory consists of the following symbols:

  1. A set of constants, such as A, B, C, ...
  2. A set of n-ary relations such as >(x, y).
  3. A set of n-ary functions such as +(x, y).
  4. An infinite set of variables such as x, y, z,...
  5. The connectives \neg, \wedge.
  6. quantifiers: \forall, \exists.
  7. parenthesis: (, ).
  8. The equality symbol = .

First-order languages are used to describe mathematics in mathematical notation with mathematical formulae.

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