Definition for "Elementary Equivalence" in the Quantum Dictionary

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

Two structures M and N (same signature) are elementarily equivalent when they satisfy exactly the same first-order sentences (no parameters); symbolically M ≡ N. Equivalence concerns sentences, not necessarily formulas with parameters.

- Mathematics & Logic -

Pure Mathematics Dictionary

A relation between two structures in the same language that they satisfy exactly the same first-order sentences; equivalently, their complete first-order theories coincide.