Two first-order structures are elementarily equivalent when they satisfy the same first-order sentences. They need not be isomorphic or embed into one another. Every elementary embedding implies elementary equivalence of its source and target.
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Elementary equivalence is a concept in model theory, a branch of mathematical logic. Two structures (or models) \( A \) and \( B \) are said to be **elementarily equivalent** if they satisfy the same first-order sentences.