# 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, $f:{\mathbb{B}}^{k}\to \mathbb{B}$.

Title | sole sufficient operator |

Canonical name | SoleSufficientOperator |

Date of creation | 2013-03-22 17:51:52 |

Last modified on | 2013-03-22 17:51:52 |

Owner | Jon Awbrey (15246) |

Last modified by | Jon Awbrey (15246) |

Numerical id | 6 |

Author | Jon Awbrey (15246) |

Entry type | Definition |

Classification | msc 03B70 |

Classification | msc 03B35 |

Classification | msc 03B22 |

Classification | msc 03B05 |

Synonym | sole sufficient connective |

Related topic | Ampheck |

Related topic | LogicalConnective |