PlanetPhysics/Sole Sufficient Operator

A sole sufficient operator or a sole sufficient connective is an [[../QuantumSpinNetworkFunctor2/|operator]] that is sufficient by itself to define all of the [[../QuantumOperatorAlgebra4/|operators]] in a specified set of operators.

In logical contexts this refers to a logical operator that suffices to define all of the [[../Predicate/|boolean-valued functions]], $f:X\to 𝔹$, where $X$ is an arbitrary set and where $𝔹$ is a generic 2-element set, typically $𝔹=\{0,1\}=\{\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{e},\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}\}$, in particular, to define all of the finitary [[../Predicate/|boolean functions]], $f:{𝔹}^k\to 𝔹$.