sole sufficient operatorSoleSufficientOperator2008-02-27 12:29:112008-04-11 17:51:34Definition% this is the default PlanetMath preamble. as your knowledge
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A \textbf{sole sufficient operator} or a \textbf{sole sufficient connective} is an operator that is sufficient by itself to define all of the operators in a specified set of operators.
In logical contexts this refers to a logical operator that suffices to define all of the Boolean-valued functions, $f : X \to \mathbb{B}$, where $X$ is an arbitrary set and where $\mathbb{B}$ is a generic 2-element set, typically $\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \}$, in particular, to define all of the finitary Boolean functions, $f : \mathbb{B}^k \to \mathbb{B}$.