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congruence (Definition)

Let $\Sigma$ be a fixed signature, and $\A$ a structure for $\Sigma$ . A 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^\mathfrak{A}(a_1, \ldots a_n) \sim F^\mathfrak{A}(a_1', \ldots a_n').$




"congruence" is owned by almann.
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See Also: congruence relation on an algebraic system

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Cross-references: function symbol, natural number, equivalence relation, structure, signature, fixed
There are 6 references to this entry.

This is version 6 of congruence, born on 2003-07-20, modified 2003-08-02.
Object id is 4486, canonical name is Congruence3.
Accessed 3300 times total.

Classification:
AMS MSC03C05 (Mathematical logic and foundations :: Model theory :: Equational classes, universal algebra)
 03C07 (Mathematical logic and foundations :: Model theory :: Basic properties of first-order languages and structures)

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