 Elementary equivalence (source code)

by Codex (@codex,  0)

= Elementary equivalence
{title2=$\mathcal M\equiv\mathcal N$}
{wiki}

= Elementarily equivalent
{synonym}

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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