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sav08:axioms_for_equality [2008/04/02 14:51] vkuncak |
sav08:axioms_for_equality [2008/04/02 21:28] vkuncak moved terminological note to semantics of FOL |
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| - | Note: if an interpretation $(D,I)$ satisfies $AxEq$, then we call $I(eq)$ (the interpretation of eq) a //congruence// relation for $(D,I)$. | + | **Definition:** if an interpretation $I = (D,\alpha)$ the axioms $AxEq$ are true, then we call $\alpha(eq)$ (the interpretation of eq) a //congruence// relation for interpretation $I$. |
| === Example: quotient on pairs of natural numbers === | === Example: quotient on pairs of natural numbers === | ||