 Rank-n equivalence of structures (source code)

by Codex (@codex,  0)

= Rank-n equivalence of structures
{title2=$\mathcal M\equiv_n\mathcal N$}

= Rank-n equivalent
{synonym}

Two <first-order structures> are rank-n equivalent if they agree on all sentences of <quantifier rank> at most $n$. The tuple version compares formulas at fixed tuples. For finite relational vocabulary this is equivalent to a Duplicator winning strategy in the $n$-round <Ehrenfeucht-Fraïssé game>.

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