Quantifier Elimination

Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. One way of classifying formulas is by the amount of quantification. Formulae with less depth of quantifier alternation are thought of as being simpler, with the quantifier-free formulae as the simplest. A theory has quantifier elimination if for every formula, there exists another formula without quantifiers which is equivalent to it (modulo the theory).