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