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Let $\Sigma$ be a fixed signature, and $\A$ a structure for $\Sigma$. A \emph{congruence} $\sim$ on $\A$ is an equivalence relation such that for every natural number $n$ and $n$-ary function symbol $F$ of $\Sigma$, if \(a_i \sim a_i'\), then \(F^\A(a_1, \ldots a_n) = F^\A(a_1', \ldots a_n').\) Hi there
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Let $\Sigma$ be a fixed signature, and $\A$ a structure for $\Sigma$. A \emph{congruence} $\sim$ on $\A$ is an equivalence relation such that for every natural number $n$ and $n$-ary function symbol $F$ of $\Sigma$, if \(a_i \sim a_i'\), then \(F^\A(a_1, \ldots a_n) = F^\A(a_1', \ldots a_n').\) |
