elementary equivalence
logic
Quick Summary
In logic, equivalence refers to a proposition formed from two others linked by "if, and only if." This means one proposition is a necessary and sufficient condition for the other. An equivalence relation in mathematics is a generalization of equality, requiring reflexivity, symmetry, and transitivity. Two structures are considered elementarily equivalent if they share the same set of true sentences. This concept is crucial in model theory, where it helps understand relationships between different mathematical structures.123
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