sole sufficient operator

A sole sufficient operator or a 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}$ .



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As of this snapshot date, this entry was owned by Jon Awbrey.