Parametric operator

In logic and mathematics, a parametric operator $$\Omega\!$$ with parameter $$\alpha\!$$ in the parametric set $$\Alpha\!$$ is a indexed family of operators $$(\Omega_{\alpha})_{\Alpha} = \{\Omega_{\alpha} : \alpha \in \Alpha\}$$ with index $$\alpha\!$$ in the index set $$\Alpha\!$$.