In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences. If N is a substructure of M, one often needs a stronger condition.
In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences. If N is a substructure of M, one often needs a stronger condition.
Source: Wikipedia "Elementary equivalence" · CC BY-SA 4.0
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