Quantifier Elimination - Related Concepts

Related Concepts

Various model theoretic ideas are related to quantifier elimination, and there are various equivalent conditions.

Every theory with quantifier elimination is model complete.

A first-order theory T has quantifier elimination if and only if for any two models B and C of T and for any common substructure A of B and C, B and C are elementarily equivalent in the language of T augmented with constants from A. In fact, it is sufficient here to show that any sentence with only existential quantifiers have the same truth value in B and C.

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