Matrix (logic)

In the predicate logic that is matrix of a formula that formula, which can all by brushing quantifiers from receives. The term is mainly used in connection with the prenex form , in which all quantifiers are at the beginning of the formula. ${\displaystyle F}$ ${\displaystyle F}$

example

The matrix of the formula

${\displaystyle \exists n\forall a(a+n=a\land \exists b.a+b=n)}$

(Existence of a neutral element of addition ) is

${\displaystyle (a+n=a)\land (a+b=n)}$.